Designed for the junior- and senior-level course in Partial Differential Equations, this new edition builds upon the solid strengths of the previous editions and has been revised to provide a more patient development of the core concepts. The material has been divided into three parts covering preliminary material, basic concepts, and advanced topics. Parts One and Two have also been reorganized and refined to provide more complete examples to help students master the content. The Sturm-Louiville Theory has been placed at the end of Chapter One and the coverage of infinite series and ordinary differential equations has been moved to an appendix.