Strange stars: Which is the ground stage of QCD at finite baryon number

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.