This book provides a short introduction to partial differential equations (PDEs). It is primarily addressed to graduate students and researchers, who are new to PDEs. The book offers a user-friendly approach to the analysis of PDEs, by combining elementary techniques and fundamental modern methods.

The author focuses the analysis on four prototypes of PDEs, and presents two approaches for each of them. The first approach consists of the method of analytical and classical solutions, and the second approach consists of the method of weak (variational)...