This lecture covers some of the advances that underpin recent progress
in deriving continuum solutions from the exact renormalization group.
Mie concentrate on concepts and on exact non-perturbative statements,
but in the process will describe how real non-perturbative calculatio
ns can be done; particularly within derivative expansion approximation
s. An effort has been made to keep the lecture pedagogical and self-co
ntained. Topics covered are the derivation of the flow equations, thei
r equivalence, continuum limits, perturbation theory, truncations, der
ivative expansions, identification of fixed points and eigenoperators,
and the role of reparametrization invariance. Some new material is in
cluded, in particular a demonstration of non-perturbative renormalizab
ility, and a discussion of ultraviolet renormalons.