  These lecture notes provide a rapid introduction to a number of rigorous
results on self-avoiding walks, with emphasis on the critical behaviour.
Following an introductory overview of the central problems, an account is given
of the Hammersley--Welsh bound on the number of self-avoiding walks and its
consequences for the growth rates of bridges and self-avoiding polygons. A
detailed proof that the connective constant on the hexagonal lattice equals
$\sqrt{2+\sqrt{2}}$ is then provided. The lace expansion for self-avoiding
walks is described, and its use in understanding the critical behaviour in
dimensions $d>4$ is discussed. Functional integral representations of the
self-avoiding walk model are discussed and developed, and their use in a
renormalisation group analysis in dimension 4 is sketched. Problems and
solutions from tutorials are included.
