The present book is the first one in the new subject area of non-integrable Hamiltonian partial differential equations, using the approach of analysis and geometry rather than algebra to study the equations. The book will be an invaluable source of information for postgraduate mathematics students and researchers working in analysis as well as for theoretical physicists interested in the topic.

For the last 20-30 years, interest among mathematicians and physicists in infinite-dimensional Hamiltonian systems and Hamiltonian partial differential equations has been growing strongly, and many papers and a number of books have been written on integrable Hamiltonian PDEs. During the last decade though, the interest has shifted steadily towards non-integrable Hamiltonian PDEs. Here, not algebra but analysis and symplectic geometry are the appropriate analysing tools. The present book is the first one to use this approach to Hamiltonian PDEs and present a complete proof of the "KAM for PDEs" theorem. It will be an invaluable source of information for postgraduate mathematics and physics students and researchers.