The present volume is an updated version of the book edited by C N Yang and M L Ge on the topics of braid groups and knot theory, which are related to statistical mechanics. This book is based on the 1989 volume but has new material included and new contributors. Contents: On the Combinatorics of Vassiliev Invariants "(J S Birman)"Solvable Methods, Link Invariants and Their Applications to Physics "(T Deguchi & M Wadati)"Quantum Symmetry in Conformal Field Theory by Hamiltonian Methods "(L D Faddeev)"Yang-Baxterization & Algebraic Structures "(M L Ge, K Xue, Y S Wu)"Spin Networks, Topology and Discrete Physics "(L H Kauffman)"Tunnel Numbers of Knots and Jones-Witten Invariants "(T Kohno)"Knot Invariants and Statistical Mechanics: A Physicist's Perspective "(F Y Wu)"and other papers Readership: Mathematical physicists.