The goal of this set of lectures is to provide an introduction to some current themes of research in quantum many-body theory in condensed matter physics. The lectures will be primarily aimed at a non-specialist audience and I will try to emphasize the main results and open questions, while minimizing the technical derivations. The tentative plan is : 1) Introduction to strongly correlated systems. – From Fermi liquids to Mott insulators. – Examples of Mott insulators in solid state and atomic physics. – Doping a Mott insulator : the example of high-temperature superconductors. 2) Quantum impurity models in equilibrium. – Kondo and Anderson models. Kondo effect. – Methods of solutions of quantum impurity models. – Introduction to Dynamical Mean Field Theory and its applications. 3) Quantum impurity models out-of-equilibrium. – Schwinger-Keldysh formalism. – Illustration on simple examples. – Wingreen-Meir formula. Kondo effect in quantum dots. (Cour organisé en collaboration avec l’Ecole Doctorale de Physique de la Région Parisienne – ED 107)

IPhT