The volume contains the lectures delivered at the “XVI Training Course in the Physics of Strongly Correlated Systems”, held in Vietri sul Mare (Salerno) Italy, in October 2011. The project of the meeting was to promote the formation of young scientists by means of training through research. These features are reflected in the book: the lectures are up-to-date monographies of relevant subjects in the field of Condensed Matter Physics. Contributions include: Strongly Correlated Electron Physics: From Kondo and Spin Glasses to Heavy Fermions, Hidden Order and Quantum Phase Transitions; Landau’s Fermi Liquid Concept to the Extreme: the Physics of Heavy Fermions; Simulations with matrix product states; The solid state as a fabric for intertwining chemical bonding, electronic structure and magnetism.