The volume develops several basic classical topics of the qualitative theory of elliptic partial differential equations and calculus of variations, including recent contributions to partial regularity for systems and the theory of viscosity solutions. The content is divided into the following five chapters: I. Variational aspects of some classes of elliptic problems; II. Classical regularity theory for linear problems; III. Interior regularity for nonlinear equations; IV. Regularity for systems; V. Viscosity solutions. The content is developed in a clear and engaging way, the derivations are very well developed, and the authors do a nice job connecting the mathematics with various applications. This volume is a very pleasant book which is strongly recommended to researchers in partial differential equations and nonlinear analysis. The book offers a rigorous introduction to a fascinating field of mathematics with multiple relevant applications to various fields.