  After a successful core collapse supernova (CCSN) explosion, a hot dense
proto-neutron star (PNS) is left as a remnant. Over a time of twenty or so
seconds, this PNS emits the majority of the neutrinos that come from the CCSN,
contracts, and loses most of its lepton number. This is the process by which
all neutron stars in our galaxy are likely born. The emitted neutrinos were
detected from SN 1987A and they will be detected in much greater numbers from
any future galactic CCSN. These detections can provide a direct window into the
properties of the dense matter encountered inside neutron stars, and they can
affect nucleosynthesis in the mate- rial ejected during the CCSN. In this
chapter, we review the basic physics of PNS cooling, including the basic
equations of PNS structure and neutrino diffusion in dense matter. We then
discuss how the nuclear equation of state, neutrino opacities in dense matter,
and convection can shape the temporal behavior of the neutrino signal. We also
discuss what was learned from the late time SN 1987A neutrinos, the prospects
for detection of these neutrinos from future galactic CCSNe, and the effects
these neutrinos can have on nucleosynthesis.
