  We present an analysis of the discovery reach for supersymmetric particles at
the upgraded Tevatron collider, assuming that SUSY breaking results in
universal soft breaking parameters at the grand unification scale, and that the
lightest supersymmetric particle is stable and neutral. We first present a
review of the literature, including the issues of unification, renormalization
group evolution of the supersymmetry breaking parameters and the effect of
radiative corrections on the effective low energy couplings and masses of the
theory. We consider the experimental bounds coming from direct searches and
those arising indirectly from precision data, cosmology and the requirement of
vacuum stability. The issues of flavor and CP-violation are also addressed. The
main subject of this study is to update sparticle production cross sections,
make improved estimates of backgrounds, delineate the discovery reach in the
supergravity framework, and examine how this might vary when assumptions about
universality of soft breaking parameters are relaxed. With 30 fb$^{-1}$
luminosity and one detector, charginos and neutralinos, as well as third
generation squarks, can be seen if their masses are not larger than 200-250
GeV, while first and second generation squarks and gluinos can be discovered if
their masses do not significantly exceed 400 GeV. We conclude that there are
important and exciting physics opportunities at the Tevatron collider, which
will be significantly enhanced by continued Tevatron operation beyond the first
phase of Run II.
