Partial Differential Equations (PDEs) are used extensively to solve engineering problems or to model scientific phenomena.  A distinctive characteristic of PDEs is the fact that solution methods are very long.  For example, to develop a typical solution takes 30-40 minutes of class time, and one typical homework problem is 4-5 pages long.  It is not so much the end result that counts, but rather the path and the sequence of steps that lead to the result.  Therefore, it is of limited help to students if only the final answer of a problem is provided.  This book presents over 150 fully solved problems with complete solutions and commentaries along the way and relates them back to the discussed theory and  applications. This approach is immensely beneficial to the students with varied mathematical backgrounds.  While an emphasis is on the fully solved problems, the authors also present the full theory as it is typically covered in a beginning PDE course.  The motivation behind the book was to develop a text that is accessible to 100% of the students regardless of their background or mathematical sophistication.  The choice of topics is based on more than 28 years of experience in teaching these courses, and the book includes material typically covered in an introductory PDE course.  The content includes a classification of PDEs, heat equation, wave equation, Laplaces equation, separation of variables, Fourier series, classical PDEs, Sturm-Liouville problems, special functions, transform methods, and the method of characteristics for first order PDEs.