Neutron stars are among the densest objects in the universe, formed from the remnants of massive stars in supernova explosions. They have masses of about 1.5 solar masses, radii of ~12 km, and central densities up to 5-10 times nuclear equilibrium density. Neutron stars are ideal laboratories for studying dense matter physics, connecting nuclear, particle, and astrophysics. They may contain exotic states like hyperons, quark matter, superfluidity, and superconductivity. Observations of binary pulsars, thermal emissions, glitches, and quasi-periodic oscillations provide insights into their masses, radii, temperatures, and compositions. Neutron stars are composed of neutrons, protons, and electrons, with possible exotic components at high densities. They can be classified into "normal" stars with hadronic matter or "strange quark matter" (SQM) stars. SQM stars, if they exist, could have unique properties, such as high density and potential for self-bound structures. The maximum mass of a neutron star is uncertain but lies between 1.44 and 3 solar masses. The minimum stable mass is about 0.1 solar masses, though this is influenced by their formation in supernovae. Neutron stars form from the gravitational collapse of massive stars, leading to a supernova explosion. The proto-neutron star formed in this process may collapse into a black hole if its mass exceeds the maximum limit. Neutrino emission plays a crucial role in the cooling of neutron stars, with the energy loss primarily occurring through neutrino emission. The cooling process is influenced by factors such as superfluidity, envelope composition, and the presence of exotic matter. The global structure of neutron stars is determined by the equations of hydrostatic equilibrium, with the TOV equations describing their behavior. The mass-radius relationship is sensitive to the equation of state (EOS) of neutron star matter, which is uncertain due to the complexity of nuclear interactions at high densities. The symmetry energy function, which describes the energy of nuclear matter, is a key factor in determining the EOS and the properties of neutron stars. The internal structure of neutron stars includes the inner and outer cores, crust, envelope, and atmosphere. The crust contains nuclei, with compositions varying with density. The core may contain exotic particles like hyperons or quark matter. The crust can exhibit superfluidity, which affects the cooling of neutron stars and can lead to glitches in pulsar timing. Neutron star cooling is primarily governed by neutrino emission, with the direct Urca process being the most efficient. However, the presence of superfluidity and the composition of the envelope can influence the cooling rate. The effective temperature of a neutron star is determined by its internal temperature and redshift effects. Observations of thermal emissions from neutron stars provide insights into their surface temperatures and cooling histories. Pulsars provide valuable information about neutron star properties, includingNeutron stars are among the densest objects in the universe, formed from the remnants of massive stars in supernova explosions. They have masses of about 1.5 solar masses, radii of ~12 km, and central densities up to 5-10 times nuclear equilibrium density. Neutron stars are ideal laboratories for studying dense matter physics, connecting nuclear, particle, and astrophysics. They may contain exotic states like hyperons, quark matter, superfluidity, and superconductivity. Observations of binary pulsars, thermal emissions, glitches, and quasi-periodic oscillations provide insights into their masses, radii, temperatures, and compositions. Neutron stars are composed of neutrons, protons, and electrons, with possible exotic components at high densities. They can be classified into "normal" stars with hadronic matter or "strange quark matter" (SQM) stars. SQM stars, if they exist, could have unique properties, such as high density and potential for self-bound structures. The maximum mass of a neutron star is uncertain but lies between 1.44 and 3 solar masses. The minimum stable mass is about 0.1 solar masses, though this is influenced by their formation in supernovae. Neutron stars form from the gravitational collapse of massive stars, leading to a supernova explosion. The proto-neutron star formed in this process may collapse into a black hole if its mass exceeds the maximum limit. Neutrino emission plays a crucial role in the cooling of neutron stars, with the energy loss primarily occurring through neutrino emission. The cooling process is influenced by factors such as superfluidity, envelope composition, and the presence of exotic matter. The global structure of neutron stars is determined by the equations of hydrostatic equilibrium, with the TOV equations describing their behavior. The mass-radius relationship is sensitive to the equation of state (EOS) of neutron star matter, which is uncertain due to the complexity of nuclear interactions at high densities. The symmetry energy function, which describes the energy of nuclear matter, is a key factor in determining the EOS and the properties of neutron stars. The internal structure of neutron stars includes the inner and outer cores, crust, envelope, and atmosphere. The crust contains nuclei, with compositions varying with density. The core may contain exotic particles like hyperons or quark matter. The crust can exhibit superfluidity, which affects the cooling of neutron stars and can lead to glitches in pulsar timing. Neutron star cooling is primarily governed by neutrino emission, with the direct Urca process being the most efficient. However, the presence of superfluidity and the composition of the envelope can influence the cooling rate. The effective temperature of a neutron star is determined by its internal temperature and redshift effects. Observations of thermal emissions from neutron stars provide insights into their surface temperatures and cooling histories. Pulsars provide valuable information about neutron star properties, including