  Phase transitions in nuclei, small atomic clusters and self-gravitating
systems demand the extension of thermo-statistics to ``Small'' systems. The
main obstacle is the thermodynamic limit. It is shown how the original
definition of the entropy by Boltzmann as the volume of the energy-manifold of
the N-body phase space allows a {\em geometrical} definition of the entropy as
function of the conserved quantities. Without invoking the thermodynamic limit
the whole ``zoo'' of phase transitions and critical points/lines can be
unambiguously defined. The relation to the Yang--Lee singularities of the
grand-canonical partition sum is pointed out. It is shown that just phase
transitions in non-extensive systems give the complete set of characteristic
parameters of the transition {\em including the surface tension.} Nuclear
heavy-ion collisions are an experimental playground to explore this extension
of thermo-statistics
