This is the second edition of the famous monograph. Besides correcting mistakes, the authors added some material. In Chapter 10 (Braids), a proof of Markov’s theorem was added. In Chapter 15 (Knots, Knot Manifolds, and Knot Groups), the Gordon-Lücke theorem on knot complements was included (without a proof). There is a new Chapter 16 (The 2-variable skein polynomial). Here we find an introduction to the HOMFLY polynomial and a self-contained exposition of basic facts on Hecke algebras. Finally, the bibliography was updated.