  The allowed parameter space for the lightest neutralino as the dark matter is
explored using the Minimal Supersymmetric Standard Model as the low-energy
effective theory without further theoretical constraints such as GUT. Selecting
values of the parameters which are in agreement with present experimental
limits and applying the additional requirement that the lightest neutralino be
in a cosmologically interesting range, we give limits on the neutralino mass
and composition. A similar analysis is also performed implementing the grand
unification constraints. The elastic scattering cross section of the selected
neutralinos on $^{27}$Al and on other materials for dark matter experiments is
discussed.
