This is a set of lecture notes for a course given at the Summer School ``Uniformisation de familles de variétés complexes'' organised by L. Meersseman in Dijon (France) August, 31-September 11, 2009 and funded by the ANR project ``Complexe'' (ANR-08-JCJC-0130-01), the École doctorale Carnot and the Institut Mathématique de Bourgogne. These notes are meant to serve as an introduction to non abelian Hodge theory with a focus on its use in the Shafarevich problem.