These lectures contain an introduction to modern renormalization group (RG)
methods as well as functional RG approaches to gauge theories. In the first
lecture, the functional renormalization group is introduced with a focus on the
flow equation for the effective average action. The second lecture is devoted
to a discussion of flow equations and symmetries in general, and flow equations
and gauge symmetries in particular. The third lecture deals with the flow
equation in the background formalism which is particularly convenient for
analytical computations of truncated flows. The fourth lecture concentrates on
the transition from microscopic to macroscopic degrees of freedom; even though
this is discussed here in the language and the context of QCD, the developed
formalism is much more general and will be useful also for other systems.Comment: 60 pages, 14 figures, Lectures held at the 2006 ECT* School
"Renormalization Group and Effective Field Theory Approaches to Many-Body
Systems", Trento, Ital
