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)