ELEMENTS OF THE CONTINUOUS RENORMALIZATION-GROUP

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.