Luigi Ambrosio is full Professor at the Scuola Normale Superiore in Pisa, Italy.
Alessandro Carlotto is Professor at the ETH Zürich in Switzerland.
Annalisa Massaccesi is Research Scholarship Holder at the Università di Verona in Italy.

The book originates from the Elliptic PDE course given by the first author at the Scuola Normale Superiore in recent years. It covers the most classical aspects of the theory of Elliptic Partial Differential Equations and Calculus of Variations, including also more recent developments on partial regularity for systems and the theory of viscosity solutions.

Variational aspects of some classes of elliptic problems.- Classical regularity theory for linear problems.- Interior regularity for nonlinear equations.- Regularity for systems.- Viscosity solutions.- Appendices - A. Some basic facts concerning Sobolev spaces.- B. Miscellaneous results in real and harmonic analysis.- C. Hausdorff measures.- D. Some tools from convex and nonsmooth analysis.