The Minimal Cooling of Neutron Stars
  A general overview of the main physical processes driving the cooling of an isolated neutron star is presented. Among the most important ones are the various possible neutrino emission processes and the occurrence of baryon pairing. Special emphasis is also put on the importance of the chemical composition of the upper layers of the star. A detailed analysis of a Minimal Scenario, which explicitly postulates that no ``exotic'' form of matter be present, is summarized and compared with presently available observational data. No striking incompatibility of the data with the predictions of the Minimal Scenario is found. Nevertheless, two, possibly three, conspicuous stars are identified which may, when better data are available, constitute strong astrophysical evidence for the occurrence of a new state of matter at high density. 
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