Preface to the First Edition; Preface to the Second Edition; Preface to the Third Edition; Preface to the Fourth Edition; Table of Contents; Part I.A Short Course of Knots and Physics; 1. Physical Knots; 2. Diagrams and Moves; 3. States and the Bracket Polynomial; 4. Alternating Links and Checkerboard Surfaces; 5. The Jones Polynomial and its Generalizations; 6. An Oriented State Model for VK(t); 7. Braids and the Jones Polynomial; 8. Abstract Tensors and the Yang-Baxter Equation; 9. Formal Feynman Diagrams, Bracket as a Vacuum-Vacuum Expectation and the Quantum Group S L(2}q.

10. The Form of the Universal R-matrix11. Yang-Baxter Models for Specializations of the Homfly Polynomial; 12. The Alexander Polynomial.; 13. Knot-Crystals -- Classical Knot Theory in a Modern Guise; 14. The Kauffman Polynomial; 15. Oriented Models and Piecewise Linear Models; 16. Three Manifold Invariants from the Jones Polynomial; 17. Integral Heuristics and Witten's Invariants; 18. Appendix -- Solutions to the Yang-Baxter Equation; Part II. Knots and Physics -- Miscellany; 1. Theory of Hitches; 2. The Rubber Band and Twisted 1\1be; 3. On a Crossing.; 4. Slide Equivalence.

5. Unoriented Diagrams and Linking Numbers6. The Penrose Chromatic Recursion; 7. The Chromatic Polynomial; 8. The Potts Model and the Dichromatic Polynomial; 9. Preliminaries for Quantum Mechanics, Spin Networks and Angular Momentum; 10. Quaternions, Cayley Numbers and the Belt Trick; 11. The Quaternion Demonstrator; 12. The Penrose Theory of Spin Networks; 13. Q-Spin Networks and the Magic Weave.; 14. Knots and Strings -Knotted Strings; 15. DNA and Quantum Field Theory; 16. Knots in Dynamical Systems -- The Lorenz Attractor ... ... . 501 Coda; References; Appendix.

IntroductionGauss Codes, Quantum Groups and Ribbon Hopf Algebras; I. Introduction; II. Knots and the Gauss Code; III. Jordan Curves and Immersed Plane Curves; IV. The Abstract Tensor Model for Link Invariants; V. From Abstract Tensors to Quantum Algebras; VI. From Quantum Algebra to Quantum Groups; VII. Categories; VIII. Invariants of 3-Manifolds; IX. Epilogue; References; Spin Networks, Topology and Discrete Physics; I. Introduction; II. Trees and Four Colors; III. The Temperley Lieb Algebra; IV. Temperley Lieb Recoupling Theory; V. Penrose Spin Networks; VI. Knots and 3-Manifolds.

VII. The Shadow WorldVIII. The Invariants of Ooguri, Crane and Yetter; References; Link Polynomials and a Graphical Calculus (with P. Vogel}; 0. Introduction; 1. Rigid Vertex Isotopy; 2. The Homfty Polynomial; 3. Braids and the Heeke Algebra; 4. Demonstration of Identities in Oriented Graphical Calculus; 5. The Dubrovnik Polynomial; REFERENCES; Knots, Tangles, and Electrical Networks (with J.R. Goldman); CONTENTS; 1. INTRODUCTION; 2. KNOTS, TANGLES, AND GRAPHS; 3. CLASSICAL ELECTRICITY; 4. MODERN ELECTRICITY-THE CONDUCTANCE INVARIANT.