Integrable Systems and Quantum Groups : Lectures Given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) Held in Montecatin

The aim of this CIME Session was to review the state of the art in the recent development of the theory of integrable systems and their relations with quantum groups. The purpose was to gather geometers and mathematical physicists to allow a broader and more complete view of these attractive and rapidly developing fields. The papers contained in this volume have at the same time the character of survey articles and of research papers, since they contain both a survey of current problems and a number of original contributions to the subject. Spectral covers, algebraically completely integrable, hamiltonian systems, and moduli of bundles.- Geometry of 2D topological field theories.- Integrals of motion and quantum groups.- Seventy years of spectral curves: 1923-1993.