  In a series of ten papers, of which this is the first, we prove that the
temperature zero renormalized perturbation expansions of a class of interacting
many-fermion models in two space dimensions have nonzero radius of convergence.
The models have "asymmetric" Fermi surfaces and short range interactions. One
consequence of the convergence of the perturbation expansions is the existence
of a discontinuity in the particle number density at the Fermi surface. Here,
we present a self contained formulation of our main results and give an
overview of the methods used to prove them.
