In this work we have examined the formation of neutron stars (NSs) in the core of arnsupernova explosion during the death of massive stars, neutrino emission mechanismsrnin the interior of NSs under di erent assumptions on their internal structure, and thernthermal history of NSs by determining neutrino luminosities and the temperature as arnfunction of time. The emphasis is made on new results such as modi ed Urca process in arnNS core with spherical nuclear structures since both momentum and energy are conservedrnin these reactions. Neutrino emission from NS cores containing exotic phases of matterrn(pion or kaon condensates,quarks) is also outlined. The e ects of neutrino emission onrnthermal histories of NSs , particularly cooling isolated stars, are examined