What can nuclear collisions teach us about the boiling of water or the formation of multi-star systems ?

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