I -- Fermi Liquid in D ? 2 -- Effective Actions and the Renormalization Group -- II -- Electronic Systems in d = 1 -- Bosonization. Luttinger Liquid -- Correspondence from Discrete to Continuum Models -- III -- From the Cuprate Compounds to the Hubbard Model -- The Mott Transition and the Hubbard Model -- Strong Coupling Limit and Some Exact Results -- Resonating Valence Bond States and High-T c Superconductivity -- The Hubbard Model at D = 1 -- New and Old Real-Space Renormalization Group Methods for Quantum Lattice Hamiltonians.

The goal of these courses is to give the non-specialist an introduction to some old and new ideas in the field of strongly correlated systems, in particular the problems posed by the high-Tc superconducting materials. The starting viewpoint to address the problem of strongly correlated fermion systems and related issues of modern condensed matter physics is the renormalization group approach applied to quantum field theory and statistical physics. The authors review the essentials of the Landau Fermi liquid theory, they discuss the 1d electron systems and the Luttinger liquid concept using different techniques: the renormalization group approach, bosonization, and the correspondence between exactly solvable lattice models and continuum field theory. Finally they present the basic phenomenology of the high-Tc compounds and different theoretical models to explain their behaviour.