The Graduate Studies in Mathematics series is made up of books useful as graduate-level course texts. This book is an introduction to the theory of quantum groups. The main topic is the quantized enveloping algebras introduced independently by Drinfeld and Jimbo. Jantzen considers the crystal (or canonical) bases discovered independently by Lusztig and Kashiwara and looks at the quantum analogue of the Lie algebar SL and then at the quantum analogue of arbitrary finite dimensional complex Lie algebras.