We give a self-contained derivation of the differential equations for Wilso
n's renormalization group for the one-particle irreducible Green functions
in fermionic systems. The application of this equation to the (t, t')-Hubba
rd model appears in Ref. 9). Here we focus on theoretical aspects. After de
riving the equations, we discuss the restrictions imposed by symmetries on
the effective action. We discuss scaling properties due to the geometry of
the Fermi surface and give precise criteria to determine when they justify
the use of one-loop flows. We also discuss the relationship of this approac
h to other RG treatments, as well as aspects of the practical treatment of
truncated equations, such as the projection to the Fermi surface and the ca
lculation of susceptibilities.