The lectures in this volume were given as part of a NATO Advanced Study Institute From finite to infinite dimensional dynamical systems held at the Isaac Newton Institute for Mathematical Sciences, Cambridge, U. K., between 21 August and 1 September 1995. The NATO ASI brought together over sixty young scientists and mathematicians from all over the world to listen to expository talks from leading experts in the field, and also gave them the opportunity to present some of their own results as posters or as lectures. We hope that what they learned both formally and in informal conversations,...