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The perturbation expansion for a general class of many-fermion systems with anon-nested, non-spherical Fermi surface is renormalized to all orders. In thelimit as the infrared cutoff is removed, the counterterms converge to a finitelimit which is differentiable in the band structure. The map from therenormalized to the bare band structure is shown to be locally injective. A newclassification of graphs as overlapping or non-overlapping is given, andimproved power counting bounds are derived from it. They imply that the onlysubgraphs that can generate $r$ factorials in the $r^{\rm th}$ order of therenormalized perturbation series are indeed the ladder graphs and thus give aprecise sense to the statement that `ladders are the most divergent diagrams'.Our results apply directly to the Hubbard model at any filling except forhalf-filling. The half-filled Hubbard model is treated in another place.Comment: plain TeX with postscript figures in a uuencoded gz-compressed tar  file. Put it on a separate directory before unpacking, since it contains  about 40 files. If you have problems, requests or comments, send e-mail to  manfred@math.ethz.c

Pertubation theory around nonnested fermi surfaces. I. Keeping the fermi surface fixed