Invitation to knot theory : virtual and classical / Heather A. Dye.

Includes bibliographical references and index.

Front Cover; Dedication; Contents; List of Figures; List of Tables; Preface; Acknowledgments; About the author; Symbol List; Section I --
Knots and crossings;
Chapter 1 Virtual knots and links;
Chapter 2 Linking invariants;
Chapter 3 A multiverse of knots;
Chapter 4 Crossing invariants;
Chapter 5 Constructing knots;
Section II Knot polynomials;
Chapter 6 The bracket polynomial;
Chapter 7 Surfaces;
Chapter 8 Bracket polynomial II;
Chapter 9 The checkerboard framing;
Chapter 10 Modifications of the bracket polynomial;
Section III Algebraic structures
Chapter 11 Quandles;
Chapter 12 Knots and quandles;
Chapter 13 Biquandles;
Chapter 14 Gauss diagrams;
Chapter 15 Applications;
Appendices.

The text begins with an introduction to virtual knots and counted invariants. It then covers the normalized f-polynomial (Jones polynomial) and other skein invariants before discussing algebraic invariants, such as the quandle and biquandle. The book concludes with two applications of virtual knots: textiles and quantum computation.