  Witten's conjecture about strange quark matter (`Strange Matter') being the
ground state of QCD at finite baryon number is presented and stars made of
strange matter (`Strange Stars') are compared to neutron stars. The only
observable way in which a strange star differs from a neutron star is in its
early thermal history and a detailed study of strange star cooling is reported
and compared to neutron star cooling. One concludes that future detection of
thermal radiation from the compact object produced in the core collapse of SN
1987A could present the first evidence for strange matter.
