  This is an expanded version of a lecture given at the {\it Workshop on
Theoretical Methods for Strongly Correlated Fermions}, held at the {\it Centre
de Recherches Math\'ematiques}, in Montr\'eal, from May 26 to May 30, 1999.
After general comments on the relevance of field theory to condensed matter
systems, the continuum description of interacting electrons in 1D is
summarized. The bosonization procedure is then introduced heuristically, but
the precise quantum equivalence between fermion and boson is also presented.
Then the exact solution of the Tomonaga-Luttinger model is carried out. Two
other applications of bosonization are then sketched. We end with a quick
introduction to non-Abelian bosonization.
