  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 $K_{\rho}$, 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.
