title: Classical and non-classical tools for minimal surfaces.

4 lectures at the "Fifth Summer School in Analysis and Applied 
Mathematics". Universitˆ La Sapienza, Roma, June 1-5, 2009.

abstract: In the first part of this series of lectures I will recall 
the basic notions from classical Complex Analysis, Differential Geometry 
and Calculus of Variations which are used in studying minimal surfaces 
and area-minimizing problems, both in the parametric and intrinsic 
approach (area formula, conformal maps in the plane, Riemann mapping 
theorem, mean curvature and Gauss curvature of a surface, first variation 
of the area). 
This should cover in particular most of the background material needed 
for the lectures delivered in parallel by Stefan Hildebrandt.
The last two lectures contain an introduction to the theory of Finite 
Perimeter Sets, including the main results of the theory (compactness, 
structure of distributional derivative, rectifiability) and a brief 
outline of few applications, namely existence results for minimal 
surfaces and capillarity problems.