I give a brief introduction to Luttinger liquids. Luttinger liquids are
paramagnetic one-dimensional metals without Landau quasi-particle excitations.
The elementary excitations are collective charge and spin modes, leading to
charge-spin separation. Correlation functions exhibit power-law behavior. All
physical properties can be calculated, e.g. by bosonization, and depend on
three parameters only: the renormalized coupling constant Kρ, and the
charge and spin velocities. I also discuss the stability of Luttinger liquids
with respect to temperature, interchain coupling, lattice effects and phonons,
and list important open problems.Comment: 10 pages, 2 figures, to be published in the Proceedings of the
International Winterschool on Electronic Properties of Novel Materials 2000,
Kirchberg, March 4-11, 200