Nearly Integrable Infinite Dimensional Hamiltonian Systems The book is devoted to partial differential equations of Hamiltonian form close to integrable equations. For such equations a KAM like theorem is proved stating that solutions of the unperturbed equation that are quasiperiodic in time mostly persist in the perturbed one. The theorem is applied to classical nonlinear PDEs with one dimensional space variable such as the nonlinear string and nonlinear Schr|dinger equation andshow that the equations have regular (=time quasiperiodic and time periodic) solutions in rich supply. These results cannot be obtained by other techniques. The book will thus be of interest to mathematicians and physicists working with nonlinear PDEs. An extensivesummary of the results and of related topics is provided in the Introduction. All the nontraditional material used is discussed in the firstpart of the book and in five appendices