Anyone with an interest in the physics of strongly correlated systems will find this an essential text. This volume contains the lectures delivered at the 11^th Trainign Course in the subject, held in Vietri sul Mare Italy, in October 2006. The aim of the course was to promote the training of young researchers in this particular field of condensed matter physics and the lectures were delivered by world-class senior researchers and include up-to-the-minute treatments of key topics.