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.
The aim of this CIME session was to review the state of the art in the 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 fields. The papers in this volume act as survey articles and research papers, as they contain both a survey of problems and a number of original contributions to the subject.