  This lecture notes are an expanded version of the course given at the
ERC-School on Geometric Measure Theory and Real Analysis, held in Pisa,
September 30th - October 30th 2013. The lectures aim to explain the main steps
of a new proof of the partial regularity of area minimizing integer rectifiable
currents in higher codimension, due originally to F. Almgren, which is
contained in a series of papers in collaboration with C. De Lellis (University
of Zurich).
