Revised second edition. The text covers the material presented for a graduate-level course on quantum groups at Harvard University. Covered topics include: Poisson algebras and quantization, Poisson-Lie groups, coboundary Lie bialgebras, Drinfelds double construction, Belavin-Drinfeld classification, Infinite dimensional Lie bialgebras, Hopf algebras, Quantized universal enveloping algebras, formal groups and h-formal groups, infinite dimensional quantum groups, the quantum double, tensor categories and quasi Hopf-algebras, braided tensor categories, KZ equations and the Drinfeld Category, Quasi-Hpf enveloping algebras, Lie associators, Fiber functors and Tannaka-Driein duality, Quantization of finite Lie bialgebras, Universal constructions, Universal quantization, Dequantization and the equivalence theorem, KZ associator and multiple zeta functions, and Mondoromy of trigonometric KZ equations. Probems are given with each subject and an answer key is included. New paperback re-issue of the revised second edition.