Presenting the numerical methods necessary to computerize optimal control processes, this reference discusses theoretical approaches to the study of optimal control problems governed by nonlinear parabolic systems, including semilinear equations, variational inequalities, and systems with phase transitions. Several examples are worked out in detail to demonstrate the usefulness of the proposed methods. To make the book more accessible, brief presentations of linear or nonlinear evolution equations, numerical approximation via finite elements, and convex control problems are included.