  The main stages in the evolution of a neutron star, from its birth as a
proto-neutron star, to its old age as a cold, catalyzed configuration, are
described. A proto-neutron star is formed in the aftermath of a successful
supernova explosion and its evolution is dominated by neutrino diffusion. Its
neutrino signal is a valuable diagnostic of its internal structure and
composition. During its transformation from a hot, lepton-rich to a cold,
catalyzed remnant, the possibility exists that it can collapse into a black
hole, which abruptly terminates neutrino emissions. The essential microphysics,
reviewed herein, that controls its evolution are the equation of state of dense
matter and its associated neutrino opacities. Several simulations of the
proto-neutron star evolution, involving different assumptions about the
composition of dense matter, are described. After its evolution into a nearly
isothermal neutron star a hundred or so years after its birth, it may be
observable through its thermal emission in X-rays during its life in the next
million years. Its surface temperature will depend upon the rapidity of
neutrino emission processes in its core, which depends on the composition of
dense matter and whether or not its constituents exhibit superfluidity and
superconductivity. Observations of thermal emission offer the best hope of a
determination of the radius of a neutron star. The implications for the
underlying dense matter equation of state of an accurate radius determination
are explored.
