The perturbation expansion for a general class of many-fermion systems with a nonnested, nonspherical Fermi surface is renormalized to all orders. In the limit as the infrared cutoff is removed, the counterterms converge to a finite limit which is differentiable in the band structure. The map From the renormalized to the bare band structure is shown to be locally injective. A new classification of graphs as overlapping or nonoverlapping is given, and improved power counting bounds are derived from it. They imply that the only subgraphs that can generate r factorials in the rth order of the renormalized perturbation series are indeed the ladder graphs and thus give a precise sense to the statement that ''ladders are the most divergent diagrams.'' Our results apply directly to the Hubbard model at any filling except for half-filling. The half-filled Hubbard model is treated in another place.
