  A detailed analysis of dark matter event rates in minimal supergravity models
(MSGM) is given. It is shown analytically that the lightest neutralino the
${{\tilde {Z}_{1}}}$ is the LSP over almost all of the parameter space, and
hence the natural candidate for cold dark matter (CDM). The radiative breaking
of $SU(2)\times U(1)$ constraints are shown to be crucial in determining the
expected event rates. Approximate analytic formulae are obtained to determine
the gaugino-higgsino content of the ${{\tilde{Z}_{1}}}$ particle.From this one
can deduce the behavior of the event rates as one varies the SUSY soft breaking
parameters and tan $\beta$. The constraint on the event rates due to the
recently measured $b\rightarrow s+\gamma$ decay is calculated. It is seen that
this data eliminates most of the parameter space where $\mu$ (the Higgs mixing
parameter) and $A_t$ (the t-quark cubic soft breaking parameter) have the same
sign. Since the t-quark is close to its Landau pole, $A_t$ is restricted to be
mostly positive, and so most of the $\mu>0$ part of the parameter space is
eliminated...
