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.
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