The book is devoted to partial differential equations ofHamiltonian form, close to integrable equations. For suchequations a KAM-like theorem is proved, stating thatsolutions of the unperturbed equation that are quasiperiodicin time mostly persist in the perturbed one. The theorem isapplied to classical nonlinear PDE's with one-dimensionalspace variable such as the nonlinear string and nonlinearSchr|dinger equation andshow that the equations have"regular" (=time-quasiperiodic and time-periodic) solutionsin rich supply.These results cannot be obtained by other techniques. Thebook will thus be of interest to mathematicians andphysicists working with nonlinear PDE's.An extensivesummary of the results and of related topics isprovided in the Introduction. All the nontraditionalmaterial used is discussed in the firstpart of the book andin five appendices.