Lectures on Integrable Systems

Mainly drawing on explicit examples, the author introduces
the reader to themost recent techniques to study finite and
infinite dynamical systems.         Without any knowledge of
differential geometry or lie groups theory the      student can
follow in a series of case studies the most                              recent
developments. r-matrices for Calogero-Moser systems and                     Toda
lattices are derived. Lax pairs for nontrivial infinite
dimensionalsystems are constructed as limits of classical
matrix algebras. The reader   will find explanations of the
approach to integrable field theories, to      spectral transform
methods and to solitons. New methods are proposed,         thus
helping students not only to understand established
techniques but also to interest them in modern research on
dynamical systems.