This textbook presents the most important topics from PDE theory. It is suitable for a two-semester course for students who have basic skills with ordinary differential equations, multivariable calculus and surface integration. The material presented in the book is arranged according to methods of solving PDE. Each chapter is introduced with a Prelude motivating the themes of the chapters: Introduction, The Big Three PDEs, Fourier series, Solving the Big Three PDEs, Characteristics, Integral transforms, Bessel Functions and Orthogonal Polynomials, Sturm-Liouville Theory and Generalized Fourier Series, PDEs in Higher dimensions, Nonhomogeneous Problems and Green’s Functions and Numerical Methods. The book has several appendices providing supplementary tools and information (Uniform Convergence; Differentiation and Integration of Fourier Series; Other Important Theorems; Existence and Uniqueness Theorems; A Menagerie of PDEs). The material presented is supplemented with many examples and selected exercises are answered at the end of the book. Some exercises are also partially formulated (mainly the plotting part) as MATLAB tasks. The MATLAB codes for figures and exercises are included in an appendix. The MATLAB source files are available on-line on the publisher’s web pages. The book presents very useful material and can be used as a basic text for self-study of PDEs.