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 IRMA Lectures in Mathematics and Theoretical Physics 2007; 141 pp; softcover Volume: 12 ISBN-10: 3-03719-047-7 ISBN-13: 978-3-03719-047-0 List Price: US$52 Member Price: US$41.60 Order Code: EMSILMTP/12 The volume starts with a lecture course by P. Etingof on tensor categories (notes by D. Calaque). This course is an introduction to tensor categories, leading to topics of recent research such as realizability of fusion rings, Ocneanu rigidity, module categories, weak Hopf algebras, Morita theory for tensor categories, lifting theory, categorical dimensions, Frobenius-Perron dimensions, and the classification of tensor categories. The remainder of the book consists of three detailed expositions on associators and the Vassiliev invariants of knots, classical and quantum integrable systems and elliptic algebras, and the groups of algebra automorphisms of quantum groups. The preface puts the results presented in perspective. Directed at research mathematicians and theoretical physicists as well as graduate students, the volume gives an overview of the ongoing research in the domain of quantum groups, an important subject of current mathematical physics. A publication of the European Mathematical Society. Distributed within the Americas by the American Mathematical Society. Readership Graduate students and research mathematicians interested in mathematicial physics. Table of Contents D. Calaque and P. Etingof -- Lectures on tensor categories J. Lieberum -- The Drinfeld associator of gl(1|1) A. Odesskii and V. Rubtsov -- Integrable systems associated with elliptic algebras N. Andruskiewitsch and F. Dumas -- On the automorphisms of $$U^+_q(\mathfrak{g})$$