The book contains concise descriptions of solution methods of partial differential equations including the types of hyperbolic, parabolic, elliptical equations, and the methods of separation of variables and of Green's functions as well as eigen analysis. A good reference for studying wave equations, heat equations, Sturm-Liouville equations as well as Laplace equations in 1-, 2-, and 3-dimensions. It contains more than 50 examples with detailed solutions throughout the text while more than 100 homework sets and midterm and final exams problems were also carefully chosen and solved. As a compressed summer course textbook, it can be expanded to be a full semester textbook in PDEs for middle level graduate students. It can also be a useful self-study guide for graduate students in physics and engineering sciences requiring PDEs. It is a handy reference for mature physicists, engineers and applied mathematicians to refresh PDEs and their solutions methods.