The quantum groups investigated in this book are quantum enveloping algebras defined by their Drinfeld-Jimbo presentation once a generalized Cartan matrix is specified. The book consists of 14 chapters arranged in five parts on quivers and their representations, quantized algebras, representations of symmetric groups, Ringel-Hall algebras, and the BLM algebra. These are complemented by an introductory chapter on two realizations of Cartan matrices, and three appendices on varieties and affine algebraic groups, quantum linear groups through coordinate algebras, and quasi-hereditary and cellular algebras. Chapters and appendices include 8-10 pages of exercises and notes, ranging from routine sketches of proofs to recent results from current literature. The book is suitable for advanced graduate students. Annotation ©2009 Book News, Inc., Portland, OR (booknews.com)