In 2013, a school on Geometric Measure Theory and Real Analysis, organized by G. Alberti, C. De Lellis and myself, took place at the Centro De Giorgi in Pisa, with lectures by V. Bogachev, R. Monti, E. Spadaro and D. Vittone.The book collects the notes of the courses. The courses provide a deep and up to date insight on challenging mathematical problems and their recent developments: infinite-dimensional analysis, minimal surfaces and isoperimetric problems in the Heisenberg group, regularity of sub-Riemannian geodesics and the regularity theory of minimal currents in any dimension and codimension.

Vladimir I. Bogachev: Sobolev classes on infinite-dimensional spaces.- Roberto Monti: Isoperimetric problem and minimal surfaces in the Heisenberg group.- Emanuele Spadaro: Regularity of higher codimension area minimizing integral currents.- Davide Vittone: The regularity problem for sub-Riemannian geodesics.