From the lecturer

R.C. would like to thank the organizer Dr. James Montaldi of the Mechanics and Symmetry Euro Summer School which was held in Peyresq, France in September 2–16, 2000 for inviting him to give several lectures on integrable Hamiltonian systems.

The principal printed source which should be read along with these notes is the “blue book”.

Avant propos

It is a great pleasure for me to introduce these lecture notes. In the last few years after our first meeting in 1997 I have been constantly learning from Richard Cushman and am glad to be one of his co-workers. What I appreciate the most in Richard's lectures and in his work is that he presents and studies modern mathematics based on examples of concrete dynamical systems which he considers in great detail. As such his approach is very accessible to physicists and practitioners.

The five lectures are presented in the way they were given, except for interchanging Lecture IV and V back to their intended logical order. Some comments and discussion are added separately at the end of each lecture. The idea of these lecture notes is to give a very informal introduction to Richard's work. We even tried to preserve some of the style of Richard's presentation peppered with such phrases as “don't be caught dead in the water”,“you will eat crow”,“sneaky gadget”,“dirty trick”, “this is deep”, etc.