Knot Theory

Abstract

Knot theory now plays a large role in modern mathematics. This unparalleled monograph describes the main concepts of modern knot theory with full proofs that are understandable to both beginners and professionals alike. It presents both old and new knot theory for consideration, as well as the most significant results from braid theory, such as the full proof of Markov's theorem, as well as Alexander's and Vogel's algorithms. In addition, it includes valuable information on the theory of coding knots by d- diagrams, as well as the author's own results in the virtual knot theory. The description of the material is accessible for undergraduate students, and the text is well suited for a course book on knots.