Invariants And Pictures

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Invariants And Pictures: Low-dimensional Topology And Combinatorial Group Theory

Author : Vassily Olegovich Manturov
Publisher : World Scientific
ISBN 13 : 9811220131
Total Pages : 387 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Invariants And Pictures: Low-dimensional Topology And Combinatorial Group Theory by : Vassily Olegovich Manturov

Download or read book Invariants And Pictures: Low-dimensional Topology And Combinatorial Group Theory written by Vassily Olegovich Manturov and published by World Scientific. This book was released on 2020-04-22 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains an in-depth overview of the current state of the recently emerged and rapidly growing theory of Gnk groups, picture-valued invariants, and braids for arbitrary manifolds. Equivalence relations arising in low-dimensional topology and combinatorial group theory inevitably lead to the study of invariants, and good invariants should be strong and apparent. An interesting case of such invariants is picture-valued invariants, whose values are not algebraic objects, but geometrical constructions, like graphs or polyhedra.In 2015, V O Manturov defined a two-parametric family of groups Gnk and formulated the following principle: if dynamical systems describing a motion of n particles possess a nice codimension 1 property governed by exactly k particles then these dynamical systems possess topological invariants valued in Gnk.The book is devoted to various realisations and generalisations of this principle in the broad sense. The groups Gnk have many epimorphisms onto free products of cyclic groups; hence, invariants constructed from them are powerful enough and easy to compare. However, this construction does not work when we try to deal with points on a 2-surface, since there may be infinitely many geodesics passing through two points. That leads to the notion of another family of groups — Γnk, which give rise to braids on arbitrary manifolds yielding invariants of arbitrary manifolds.

Representations and Invariants of the Classical Groups

Author : Roe Goodman
Publisher : Cambridge University Press
ISBN 13 : 9780521663489
Total Pages : 708 pages
Book Rating : 4.6/5 (634 download)

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Book Synopsis Representations and Invariants of the Classical Groups by : Roe Goodman

Download or read book Representations and Invariants of the Classical Groups written by Roe Goodman and published by Cambridge University Press. This book was released on 2000-01-13 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: More than half a century has passed since Weyl's 'The Classical Groups' gave a unified picture of invariant theory. This book presents an updated version of this theory together with many of the important recent developments. As a text for those new to the area, this book provides an introduction to the structure and finite-dimensional representation theory of the complex classical groups that requires only an abstract algebra course as a prerequisite. The more advanced reader will find an introduction to the structure and representations of complex reductive algebraic groups and their compact real forms. This book will also serve as a reference for the main results on tensor and polynomial invariants and the finite-dimensional representation theory of the classical groups. It will appeal to researchers in mathematics, statistics, physics and chemistry whose work involves symmetry groups, representation theory, invariant theory and algebraic group theory.

2D and 3D Image Analysis by Moments

Author : Jan Flusser
Publisher : John Wiley & Sons
ISBN 13 : 1119039355
Total Pages : 555 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis 2D and 3D Image Analysis by Moments by : Jan Flusser

Download or read book 2D and 3D Image Analysis by Moments written by Jan Flusser and published by John Wiley & Sons. This book was released on 2016-12-19 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents recent significant and rapid development in the field of 2D and 3D image analysis 2D and 3D Image Analysis by Moments, is a unique compendium of moment-based image analysis which includes traditional methods and also reflects the latest development of the field. The book presents a survey of 2D and 3D moment invariants with respect to similarity and affine spatial transformations and to image blurring and smoothing by various filters. The book comprehensively describes the mathematical background and theorems about the invariants but a large part is also devoted to practical usage of moments. Applications from various fields of computer vision, remote sensing, medical imaging, image retrieval, watermarking, and forensic analysis are demonstrated. Attention is also paid to efficient algorithms of moment computation. Key features: Presents a systematic overview of moment-based features used in 2D and 3D image analysis. Demonstrates invariant properties of moments with respect to various spatial and intensity transformations. Reviews and compares several orthogonal polynomials and respective moments. Describes efficient numerical algorithms for moment computation. It is a "classroom ready" textbook with a self-contained introduction to classifier design. The accompanying website contains around 300 lecture slides, Matlab codes, complete lists of the invariants, test images, and other supplementary material. 2D and 3D Image Analysis by Moments, is ideal for mathematicians, computer scientists, engineers, software developers, and Ph.D students involved in image analysis and recognition. Due to the addition of two introductory chapters on classifier design, the book may also serve as a self-contained textbook for graduate university courses on object recognition.

Foundations of Perceptual Theory

Author : S.C. Masin
Publisher : Elsevier
ISBN 13 : 9780080867533
Total Pages : 421 pages
Book Rating : 4.8/5 (675 download)

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Book Synopsis Foundations of Perceptual Theory by : S.C. Masin

Download or read book Foundations of Perceptual Theory written by S.C. Masin and published by Elsevier. This book was released on 1993-06-30 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: Historical analysis reveals that perceptual theories and models are doomed to relatively short lives. The most popular contemporary theories in perceptual science do not have as wide an acceptance among researchers as do some of those in other sciences. To understand these difficulties, the authors of the present volume explore the conceptual and philosophical foundations of perceptual science. Based on logical analyses of various problems, theories, and models, they offer a number of reasons for the current weakness of perceptual explanations. New theoretical approaches are also proposed. At the end of each chapter, dicussants contribute to the conclusions by critically examining the authors' ideas and analyses.

Visual Allusions

Author : Nicholas Wade
Publisher : Psychology Press
ISBN 13 : 9780863771309
Total Pages : 304 pages
Book Rating : 4.7/5 (713 download)

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Book Synopsis Visual Allusions by : Nicholas Wade

Download or read book Visual Allusions written by Nicholas Wade and published by Psychology Press. This book was released on 1990 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book a leading researcher and artist explores how we see pictures and how they can communicate messages to us, both directly and indirectly by making allusions to objects in space or to stored images in our minds. Dr Wade provides fascinating examples of pictures that communicate hidden messages, either by implying something else, or by a shape or portrait which is carried covertly within another design. He analyses image processing stages in vision, demonstrating that the various stages may be related to styles in representational art. He shows how the way we have been taught to look at and recognise objects, affects the way we see them. The book lavishly illustrates with original examples of visual allusions and includes detailed practical advice on how photographers and designers can create them. Essential reading for photographers, designers, artists, people in film and television, and anyone involved in visual science , visual communication and advertising.

Invariants of Behavior

Author : Mario Negrello
Publisher : Springer Science & Business Media
ISBN 13 : 1441988041
Total Pages : 252 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Invariants of Behavior by : Mario Negrello

Download or read book Invariants of Behavior written by Mario Negrello and published by Springer Science & Business Media. This book was released on 2011-06-02 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of the brain and behavior is illuminated with the discovery of invariances. Experimental brain research uncovers constancies amidst variation, with respect to interventions and transformations prescribed by experimental paradigms. Place cells, mirror neurons, event related potentials and areas differentially active in fMRI, all illustrate the pervasive role of invariances in neural systems in relation to their function.

The Perception of Pictures

Author : Margaret A. Hagen
Publisher : Academic Press
ISBN 13 : 1483259560
Total Pages : 380 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis The Perception of Pictures by : Margaret A. Hagen

Download or read book The Perception of Pictures written by Margaret A. Hagen and published by Academic Press. This book was released on 2014-05-10 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Durer's Devices: Beyond the Projective Model of Pictures is a collection of papers that discusses the nature of picture making and perception. One paper presents a perceptual theory of pictorial representation in which cultural and historical options in styles of depiction that appear to be different are actually closely related perceptually. Another paper discusses pictorial functions and perceptual structures including pictorial representation, perceptual theory, flat canvass, and the deep world. One paper suggests that perception can be more a matter of information "make up" than "pick up." Light becomes somewhat informative and the eye, correspondingly, becomes less or more presumptive. Another paper notes that human vision is transformed by our modes of representation, that image formation can be essentially incomplete, false, or misleading (primarily as regards dramatic performance and pictorial representation). One paper makes three claims that: (1) the blind have untapped depiction abilities; (2) haptics, involving the sense of touch, have an intuitive sense of perspective; and (3) depiction is perceptual based on graphic elements and pictorial configurations. The collection is suitable for psychologists, physiologists, psychophysicists, and researchers in human perception or phenomenology.

Thinking in Images

Author : Piotr Kozak
Publisher : Bloomsbury Publishing
ISBN 13 : 1350267473
Total Pages : 249 pages
Book Rating : 4.3/5 (52 download)

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Book Synopsis Thinking in Images by : Piotr Kozak

Download or read book Thinking in Images written by Piotr Kozak and published by Bloomsbury Publishing. This book was released on 2023-04-20 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: What does it mean to think with images? There is a well-established tradition of studying thought processes through the nature of language, and we know much more about thinking with language than about thinking with images. Piotr Kozak takes an important step towards rectifying this position. Presenting a unified theory of different types of images, such as diagrams, maps, technical drawings and photographs, Kozak argues that images provide a genuine and autonomous form of content and knowledge. In contrast to the propositional view of thinking and resemblance-based accounts, he puts forward a measurement-theoretic account of images as operations that exemplify measures, revealing the outcomes of measurement operations performed on a depicted situation. Bringing together insights from philosophy of science, picture-theory, cognitive science and cognitive psychology, this book demonstrates that we can only understand what an image is if we truly understand the role they play in our thought processes, challenging the prevailing view that the utility of images is only instrumental and cognitively inferior.

Moments and Moment Invariants in Pattern Recognition

Author : Jan Flusser
Publisher : John Wiley & Sons
ISBN 13 : 9780470684764
Total Pages : 312 pages
Book Rating : 4.6/5 (847 download)

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Book Synopsis Moments and Moment Invariants in Pattern Recognition by : Jan Flusser

Download or read book Moments and Moment Invariants in Pattern Recognition written by Jan Flusser and published by John Wiley & Sons. This book was released on 2009-11-04 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Moments as projections of an image’s intensity onto a proper polynomial basis can be applied to many different aspects of image processing. These include invariant pattern recognition, image normalization, image registration, focus/ defocus measurement, and watermarking. This book presents a survey of both recent and traditional image analysis and pattern recognition methods, based on image moments, and offers new concepts of invariants to linear filtering and implicit invariants. In addition to the theory, attention is paid to efficient algorithms for moment computation in a discrete domain, and to computational aspects of orthogonal moments. The authors also illustrate the theory through practical examples, demonstrating moment invariants in real applications across computer vision, remote sensing and medical imaging. Key features: Presents a systematic review of the basic definitions and properties of moments covering geometric moments and complex moments. Considers invariants to traditional transforms – translation, rotation, scaling, and affine transform - from a new point of view, which offers new possibilities of designing optimal sets of invariants. Reviews and extends a recent field of invariants with respect to convolution/blurring. Introduces implicit moment invariants as a tool for recognizing elastically deformed objects. Compares various classes of orthogonal moments (Legendre, Zernike, Fourier-Mellin, Chebyshev, among others) and demonstrates their application to image reconstruction from moments. Offers comprehensive advice on the construction of various invariants illustrated with practical examples. Includes an accompanying website providing efficient numerical algorithms for moment computation and for constructing invariants of various kinds, with about 250 slides suitable for a graduate university course. Moments and Moment Invariants in Pattern Recognition is ideal for researchers and engineers involved in pattern recognition in medical imaging, remote sensing, robotics and computer vision. Post graduate students in image processing and pattern recognition will also find the book of interest.

Computer Analysis of Images and Patterns

Author : Mario Vento
Publisher : Springer Nature
ISBN 13 : 3030298884
Total Pages : 688 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Computer Analysis of Images and Patterns by : Mario Vento

Download or read book Computer Analysis of Images and Patterns written by Mario Vento and published by Springer Nature. This book was released on 2019-08-23 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two volume set LNCS 11678 and 11679 constitutes the refereed proceedings of the 18th International Conference on Computer Analysis of Images and Patterns, CAIP 2019, held in Salerno, Italy, in September 2019. The 106 papers presented were carefully reviewed and selected from 176 submissions The papers are organized in the following topical sections: Intelligent Systems; Real-time and GPU Processing; Image Segmentation; Image and Texture Analysis; Machine Learning for Image and Pattern Analysis; Data Sets and Benchmarks; Structural and Computational Pattern Recognition; Posters.

Quantum Invariants

Author : Tomotada Ohtsuki
Publisher : World Scientific
ISBN 13 : 9789812811172
Total Pages : 516 pages
Book Rating : 4.8/5 (111 download)

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Book Synopsis Quantum Invariants by : Tomotada Ohtsuki

Download or read book Quantum Invariants written by Tomotada Ohtsuki and published by World Scientific. This book was released on 2002 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive and self-contained presentation of quantum and related invariants of knots and 3-manifolds. Polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants, i.e. invariants derived from representations of quantum groups and from the monodromy of solutions to the Knizhnik-Zamolodchikov equation. With the introduction of the Kontsevich invariant and the theory of Vassiliev invariants, the quantum invariants become well-organized. Quantum and perturbative invariants, the LMO invariant, and finite type invariants of 3-manifolds are discussed. The ChernOCoSimons field theory and the WessOCoZuminoOCoWitten model are described as the physical background of the invariants. Contents: Knots and Polynomial Invariants; Braids and Representations of the Braid Groups; Operator Invariants of Tangles via Sliced Diagrams; Ribbon Hopf Algebras and Invariants of Links; Monodromy Representations of the Braid Groups Derived from the KnizhnikOCoZamolodchikov Equation; The Kontsevich Invariant; Vassiliev Invariants; Quantum Invariants of 3-Manifolds; Perturbative Invariants of Knots and 3-Manifolds; The LMO Invariant; Finite Type Invariants of Integral Homology 3-Spheres. Readership: Researchers, lecturers and graduate students in geometry, topology and mathematical physics."

Quantum Invariants

Author : Tomotada Ohtsuki
Publisher : World Scientific
ISBN 13 : 9814490717
Total Pages : 508 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Quantum Invariants by : Tomotada Ohtsuki

Download or read book Quantum Invariants written by Tomotada Ohtsuki and published by World Scientific. This book was released on 2001-12-21 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive and self-contained presentation of quantum and related invariants of knots and 3-manifolds. Polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants, i.e. invariants derived from representations of quantum groups and from the monodromy of solutions to the Knizhnik-Zamolodchikov equation. With the introduction of the Kontsevich invariant and the theory of Vassiliev invariants, the quantum invariants become well-organized. Quantum and perturbative invariants, the LMO invariant, and finite type invariants of 3-manifolds are discussed. The Chern–Simons field theory and the Wess–Zumino–Witten model are described as the physical background of the invariants. Contents: Knots and Polynomial InvariantsBraids and Representations of the Braid GroupsOperator Invariants of Tangles via Sliced DiagramsRibbon Hopf Algebras and Invariants of LinksMonodromy Representations of the Braid Groups Derived from the Knizhnik–Zamolodchikov EquationThe Kontsevich InvariantVassiliev InvariantsQuantum Invariants of 3-ManifoldsPerturbative Invariants of Knots and 3-ManifoldsThe LMO InvariantFinite Type Invariants of Integral Homology 3-Spheres Readership: Researchers, lecturers and graduate students in geometry, topology and mathematical physics. Keywords:Kontsevich Invariant;LMO Invariant;Quantum Groups;Knot;3-Manifold;Quantum Invariant;Vassiliev Invariant;Finite Type Invariant;Chord Diagram;Jacobi Diagram;KZ Equation;Chern-Simons TheoryReviews:“This is a nicely written and useful book: I think that the author has done a great job in explaining quantum invariants of knots and 3-manifolds also on an intuitive and well-motivated, organically growing and not too technical level, at the same time however presenting a lot of material ordered by a clear guiding line.”Mathematics Abstracts “Ohtsuki's book is a very valuable addition to the literature. It surveys the full spectrum of work in the area of quantum invariants … Ohtsuk's book is very readable, for he makes an attempt to present the material in as straightforward a way as possible … the presentation here is very clear and should be easily accessible … this is an excellent book which I would recommend to beginners wanting to learn about quantum invariants and to experts alike.”Mathematical Reviews

Visual Order

Author : N. H. Freeman
Publisher : Cambridge University Press
ISBN 13 : 0521266688
Total Pages : 414 pages
Book Rating : 4.5/5 (212 download)

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Book Synopsis Visual Order by : N. H. Freeman

Download or read book Visual Order written by N. H. Freeman and published by Cambridge University Press. This book was released on 1985-11-28 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of essays researches the nature and development of pictorial representation.

Algebraic Groups and Their Birational Invariants

Author : V. E. Voskresenskii
Publisher : American Mathematical Soc.
ISBN 13 : 0821872885
Total Pages : 218 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Algebraic Groups and Their Birational Invariants by : V. E. Voskresenskii

Download or read book Algebraic Groups and Their Birational Invariants written by V. E. Voskresenskii and published by American Mathematical Soc.. This book was released on 2011-10-06 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the late 1960s, methods of birational geometry have been used successfully in the theory of linear algebraic groups, especially in arithmetic problems. This book--which can be viewed as a significant revision of the author's book, Algebraic Tori (Nauka, Moscow, 1977)--studies birational properties of linear algebraic groups focusing on arithmetic applications. The main topics are forms and Galois cohomology, the Picard group and the Brauer group, birational geometry of algebraic tori, arithmetic of algebraic groups, Tamagawa numbers, $R$-equivalence, projective toric varieties, invariants of finite transformation groups, and index-formulas. Results and applications are recent. There is an extensive bibliography with additional comments that can serve as a guide for further reading.

Advances in Information Retrieval

Author : Center for Intelligent Information Retrieval
Publisher : Springer Science & Business Media
ISBN 13 : 0792378121
Total Pages : 326 pages
Book Rating : 4.7/5 (923 download)

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Book Synopsis Advances in Information Retrieval by : Center for Intelligent Information Retrieval

Download or read book Advances in Information Retrieval written by Center for Intelligent Information Retrieval and published by Springer Science & Business Media. This book was released on 2000-04-30 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: The NSF Center for Intelligent Information Retrieval (CIIR) was formed in the Computer Science Department of the University of Massachusetts, Amherst, in 1992. Through its efforts in basic research, applied research, and technology transfer, the CIIR has become known internationally as one of the leading research groups in the area of information retrieval. The CIIR focuses on research that results in more effective and efficient access and discovery in large, heterogeneous, distributed text and multimedia databases. The scope of the work that is done in the CIIR is broad and goes significantly beyond `traditional' areas of information retrieval such as retrieval models, cross-lingual search, and automatic query expansion. The research includes both low-level systems issues such as the design of protocols and architectures for distributed search, as well as more human-centered topics such as user interface design, visualization and data mining with text, and multimedia retrieval. Advances in Information Retrieval: Recent Research from the Center for Intelligent Information Retrieval is a collection of papers that covers a wide variety of topics in the general area of information retrieval. Together, they represent a snapshot of the state of the art in information retrieval at the turn of the century and at the end of a decade that has seen the advent of the World-Wide Web. The papers provide overviews and in-depth analysis of theory and experimental results. This book can be used as source material for graduate courses in information retrieval, and as a reference for researchers and practitioners in industry.

On Images

Author : John V. Kulvicki
Publisher : Clarendon Press
ISBN 13 : 0191537454
Total Pages : 274 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis On Images by : John V. Kulvicki

Download or read book On Images written by John V. Kulvicki and published by Clarendon Press. This book was released on 2006-08-03 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Whether it was the demands of life, leisure, or a combination of both that forced our hands, we have developed a myriad of artefacts—-maps, notes, descriptions, diagrams, flow-charts, photographs, paintings, and prints—-that stand for other things. Most agree that images and their close relatives are special because, in some sense, they look like what they are about. This simple claim is the starting point for most philosophical investigations into the nature of depiction. On Images argues that this starting point is fundamentally misguided. Whether a representation is an image depends not on how it is perceived but on how it relates to others within a system. This kind of approach, first championed by Nelson Goodman in his Languages of Art, has not found many supporters, in part because of weaknesses with Goodman's account. On Images shows that a properly crafted structural account of pictures has many advantages over the perceptual accounts that dominate the literature on this topic. In particular, it explains the close relationship between pictures, diagrams, graphs and other kinds of non-linguistic representation. It undermines the claim that pictures are essentially visual by showing that audio recordings, tactile line drawings, and other non-visual representations are pictorial. Also, by avoiding explaining images in terms of how we perceive them, this account sheds new light on why pictures seem so perceptually special in the first place. This discussion of picture perception recasts some old debates on the topic, suggests further lines of philosophical and empirical research, and ultimately leads to a new perspective on pictorial realism.

Knots, Links and Their Invariants

Author : A. B. Sossinsky
Publisher : American Mathematical Society
ISBN 13 : 1470471515
Total Pages : 149 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Knots, Links and Their Invariants by : A. B. Sossinsky

Download or read book Knots, Links and Their Invariants written by A. B. Sossinsky and published by American Mathematical Society. This book was released on 2023-05-22 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an elementary introduction to knot theory. Unlike many other books on knot theory, this book has practically no prerequisites; it requires only basic plane and spatial Euclidean geometry but no knowledge of topology or group theory. It contains the first elementary proof of the existence of the Alexander polynomial of a knot or a link based on the Conway axioms, particularly the Conway skein relation. The book also contains an elementary exposition of the Jones polynomial, HOMFLY polynomial and Vassiliev knot invariants constructed using the Kontsevich integral. Additionally, there is a lecture introducing the braid group and shows its connection with knots and links. Other important features of the book are the large number of original illustrations, numerous exercises and the absence of any references in the first eleven lectures. The last two lectures differ from the first eleven: they comprise a sketch of non-elementary topics and a brief history of the subject, including many references.