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.