This book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure
theory. It features a wide variety of research topics in which a crucial role is played by the interaction of fine analytic
techniques and deep geometric observations, combining the intuitive and geometric aspects of mathematics with analytical ideas
and variational methods. The problems addressed are challenging and complex, and often require the use of several refined
techniques to overcome the major difficulties encountered. The lectures, given during the course "Partial Differential Equations
and Geometric Measure Theory'' in Cetraro, June 2-7, 2014, should help to encourage further research in the area. The enthusiasm
of the speakers and the participants of this CIME course is reflected in the text.