  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 chain. This fermion-boson
transmutation allows to describe interacting fermions as a system of coupled
oscillators. Tomonaga's model of interacting nonrelativistic fermions on a ring
is presented and first discussed in low order perturbation theory. After
introducing the concept of two independent species of right and left moving
fermions the exact solution of the Tomonaga-Luttinger model is discussed in
detail. The momentum distribution and spectral functions are calculated using
the method of the bosonization of the field operator. The general Luttinger
liquid phenomenology is shortly discussed.
