Lectures in Knot Theory

This book presents lectures on knot theory, exploring both standard and innovative topics while engaging readers in advanced mathematical concepts.

The text is grounded in lectures delivered by the first author on various aspects of knot theory, including some unconventional topics. Lectures in Knot Theory delves into contemporary themes in the field, such as skein modules, Khovanov homology, and Gram determinants, all motivated by knots. By providing an innovative perspective, this book enriches the existing body of literature. Each lecture starts with a historical context, offering motivation for the evolution of the respective subjects.

A basic understanding of topology and abstract algebra is sufficient for comprehending most of the material presented in Lectures in Knot Theory. The book caters to a diverse audience, including beginning and advanced graduate students, advanced undergraduates, and researchers who are keen on exploring knot theory and its connections to other areas of mathematics, physics, biology, and chemistry. The inclusion of numerous exercises, open problems, and conjectures serves to deepen the reader's engagement with the material.

The versatility of this text makes it suitable for various classroom settings, depending on course level and instructor preferences. The Preface offers suggestions for different course coverage options. The lecture format and broad range of topics aim to stimulate independent research and the application of the discussed methods to other scientific disciplines. Additionally, an introduction to the topology of 3-dimensional manifolds is provided in the appendices, along with a Table of Knots in Appendix C.