  The main ideas behind nuclear supersymmetry are presented, starting from the
basic concepts of symmetry and the methods of group theory in physics. We
propose new, more stringent experimental tests that probe the supersymmetry
classification in nuclei and point out that specific correlations should exist
for particle transfer intensities among supersymmetric partners. We also
discuss possible ways to generalize these ideas to cases where no dynamical
symmetries are present. The combination of these theoretical and experimental
studies may play a unifying role in nuclear phenomena.
