  This is the first of a series of three papers treating light baryon
resonances (up to 3 GeV) within a relativistically covariant quark model based
on the three-fermion Bethe-Salpeter equation with instantaneous two- and
three-body forces. In this paper we give a unified description of the
theoretical background and demonstrate how to solve the Bethe-Salpeter equation
by a reduction to the Salpeter equation. The specific new features of our
covariant Salpeter model with respect to the usual nonrelativistic quark model
are discussed in detail. The purely theoretical results obtained in this paper
will be applied numerically to explicit quark models for light baryons in two
subsequent papers.
