Semigroup approach to nonlinear diffusion equations This book is concerned with functional methods (nonlinear semigroups of contractions nonlinear m accretive operators and variational techniques) in the theory of nonlinear partial differential equations of elliptic and parabolic type. In particular applications to the existence theory of nonlinear parabolic equations nonlinear Fokker Planck equations phase transition and free boundary problems are presented in details. Emphasis is put on functional methods in partial differential equations (PDE) and less on specific results