I attempt to give a pedagogical overview of the progress which has occurred during the past decade in the description of one-dimensional correlated fermions. Fermi liquid theory based on a quasi-parti . . . . .

Table of contents 1. Introduction 2. Non-Fermi-liquid features of Fermi liquids: 1D physics in higher dimensions 3. Dzyaloshinskii-Larkin solution of the Tomonaga-Luttinger model 4. Renormalization g . . . . .

Many fundamental one-dimensional lattice models such as the Heisenberg or the Hubbard model are integrable. For these microscopic models, parameters in the Luttinger liquid theory can often be fixed a . . . . .

Coulomb interaction effects have pronounced consequences in carbon nanotubes due to their 1D nature. In particular, correlations imply the breakdown of Fermi liquid theory and typically lead to Luttin . . . . .

The theoretical description of interacting fermions in one spatial dimension is simplified by the fact that the low energy spectrum of noniteracting fermions is identical to the one of a harmonic chai . . . . .

n contrast to the well known Fermi liquid theory of three dimensions, interacting one-dimensional and quasi one-dimensional systems of fermions are described at low energy by an effective theory known . . . . .

A brief introduction to Luttinger liquids. Luttinger liquids are paramagnetic one-dimensional metals without Landau quasi-particle excitations.

In these lecture notes, the basic physics of Fermi liquids and Luttinger liquids is presented. Fermi liquids are discussed both from a phenomenological viewpoint, in relation to microscopic approaches . . . . .