This book is based on the LMS Symposium on quantum groups held at Durham in 1999; it contains papers based on lectures presented there. There are two surveys papers presenting the content of two lecture series. The first one (written by S. Ariki) contains an introduction to cyclotomic Hecke algebras using the language of Fock spaces and their relation to the study of solvable lattice models in statistical mechanics. The second one (by P. Etinghof and O. Schiffmann) contains a description of the classical and quantum dynamical Yang-Baxter equation and its applications to the theory of integrable systems and to representation theory. The book contains moreover 11 papers on various topics in the field. They are written by E. Beggs (group doublecross products), R. Carter and R. Marsh (canonical bases), V. Chari and A. Pressley (modules of quantum affine sl2), B. Drabant (balanced categories and Hopf algebras), K. R. Goodearl (quantized primitive ideal spaces), I. Gordon (quantum groups at roots of unity), J. Ding and T. J. Hodges (YB equation for operators on function fields), S. Majid (twisting of quantum groups), I. M. Musson (finite quantum groups and pointed Hopf algebras), D. Parashar and R. J. McDermott (quantum and Jordanian deformations) and H. Wenzl (tensor category and braid representations). This is an interesting collection of papers in the field.