This monograph covers the analysis and optimal control of infinite dimensional nonlinear systems of the accretive type. Many applications of controlled systems can be modelled in this form, including nonlinear elliptic and parabolic problems, variational inequalities of elliptic and parabolic type, Stefan problems and other problems with free boundaries, nonlinear hyperbolic problems and nonlinear first order partial differential equations. The control of melting and solidification processes and the optimal control of free surfaces are two examples of the types of applications that are presented in this work. The text also covers optimal control problems governed by variational inequalities and problems with free boundary and examines two complememtary aspects of theory of nonlinear infinite dimensional systems: existence of solutions and synthesis via optimality criteria. It also presents existence theory for nonlinear differential equations of accretive type in Banach spaces with applications to partial differential equations.