Quantum Electron Liquids and High Tc Superconductivity 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