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.

This book originated from a course given at the Univcrsidad Aut6noma of Madrid in the Spring of 1994 and in the Universidad Complutense of Madrid in 1995. 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-1~ superconducting materials. As theoretical physicists, our starting viewpoint to address the problem of strongly correlat­ ed ferlnion systems and related issues of modern condensed matter physics ·is the renormalization group approach applied both to quantU111 field theory and statistical physics. In recent years this has become not only a powerful tool for retrieving the essential physics of interacting systems but also a link between theoretical physics and modern condensed matter physics. Furthermore, once we have this common background for dealing with apparently different prob­ lems, we discuss more specific topics and even phenomenological aspects of the field. In doing so we have tried to make the exposition clear and simple, with­ out entering into technical details but focusing ill the fundamental physics of the phenomena under study. Therefore ,ve expect that our experience ll1ay have some value to other people entering this fascinating field. We have divided these notes into three parts and each part into chapters, which correspond roughly to one or two lectures. Part I, Chaps. 1-2 (A. H. V.

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.