Introduction

Abstract

Nonlinear systems model all but the simplest physical phenomena. In the classical theory, the tools of Poisson geometry appear in an essential way, while for quantum systems, the representation theory of Lie groups and algebras, and of the in.nite-dimensional loop and Kac-Moody algebras are basic. There is a class of nonlinear systems which are integrable, and the methods of solution for these systems draw on many .elds of mathematics. They are the subject of the lectures in this book.