A two dimensional Fermi liquid.: Part 1:: Overview

In a series of ten papers (see the flow chart at the end of I), 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.