Elliptic Curves, Hilbert Modular Forms and Galois Deformations

The notes in this volume correspond to advanced courses held at the Centre de Recerca Matem�tica as part of the research program in Arithmetic Geometry in the 2009-2010 academic year. The notes by Laurent Berger provide an introduction to p -adic Galois representations and Fontaine rings, which are especially useful for describing many local deformation rings at p that arise naturally in Galois deformation theory.