  We present a general method to study weak-coupling instabilities of a large
class of interacting electron models in a controlled and unbiased way. Quite
generally, the electron gas is unstable towards a superconducting state even in
the absence of phonons, since high-energy spin fluctuations create an effective
attraction between the quasi-particles. As an example, we show the occurrence
of d-wave pairing in the repulsive Hubbard model in two dimensions. In one
dimension or if the Fermi surface is nested, there are several competing
instabilities. The required renormalization group formalism for this case is
presented to lowest (one-loop) order on a most elementary level, connecting the
idea of the ``parquet summation'' to the more modern concept of Wilson's
effective action. The validity and restrictions of the one-loop approximation
are discussed in detail. As a result, three different renormalization group
approaches known in the literature are shown to be equivalent within the regime
of applicability. We also briefly discuss the open problem of a two-dimensional
Fermi system at Van Hove filling without nesting.
