This revised and expanded comprehensive second edition discusses mathematical models that give rise to PDEs, classifies the equations and problems into different types, and examines exact and approximate methods for solution of these problems. The book addresses problems that involve both linear and nonlinear equations of the three basic types: parabolic, hyperbolic and elliptic. The coverage ranges from solution methods for first-order PDEs to perturbation and asymptotic methods for solving linear and nonlinear higher order equations. The book also includes a substantial number of new exercises and examples, with many answers. Furthermore, the chapter order is flexible enough to be used for full-year or one-term courses. The previous edition of this book was published in 1983.