  We perform a complete analysis of the supersymmetric particle spectrum in the
Minimal Supergravity (mSUGRA) model where the soft SUSY breaking scalar masses,
gaugino masses and trilinear couplings are unified at the GUT scale, so that
the electroweak symmetry is broken radiatively. We show that the present
constraints on the Higgs boson and superparticle masses from collider searches
and precision measurements still allow for large regions of the mSUGRA
parameter space where charginos, neutralinos, sleptons and top squarks as well
as the heavier Higgs particles, are light enough to be produced at the next
generation of $\ee$ linear colliders with center of mass energy around
$\sqrt{s} \sim 800$ GeV, with sizeable cross sections. An important part of
this parameter space remains even when we require that the density of the
lightest neutralinos left over from the Big Bang, which we calculate using
standard assumptions, falls in the range favored by current determinations of
the Dark Matter density in the Universe. Already at a c.m. energy of 500 GeV,
SUSY particles can be accessible in some parameter range, and if the energy is
increased to $\sqrt{s} \simeq 1.2$ TeV, the $e^+e^-$ collider will have a reach
for high precision studies of SUSY particles in a range that is comparable to
the discovery range of the LHC.
