The present volume is concerned with the theory of partial differential equations, in particular with parts of this wide field that are related to concepts of physics and mechanics. Even with this restriction, completeness seems unattainable; to a certain extent the material selected corresponds to my personal experience and taste. The intention is to make an important branch of mathematical analysis more accessible by emphasizing concepts and methods rather than presenting a collection of theorems and facts and by leading from an elementary level to key points on the frontiers of our knowledge.