"Contains the proceedings of a NATO Advanced Research Workshop on these interrelated disciplines. The principal goal of the workshop was to advance the pace discoveries in theoretical research on the chosen topics by providing an opportunity for presentations of new results, and by providing a forum to discuss likely directions for the future work. The workshop brought together a unique combination of leading researchers in integrable systems, conformal field theory, quantum groups, and knot theory, thereby providing an opportunity for a cross-fertilization of ideas."--Preface.