Explore the fascinating world of neutron stars and black holes in this comprehensive lecture series delivered by G Srinivasan from the Raman Research Institute. Delve into the maximum mass of neutron stars, examining key concepts like neutronization of matter, the Tolman-Oppenheimer-Volkoff equation, and the limiting mass for these celestial objects. Investigate the physics behind cold stars, stability of matter, and exotic states near the center of neutron stars. Learn about Bose-Einstein statistics, condensation, and the possibility of quark-gluon soup in these extreme environments. Gain insights into the implosion of stars in General Relativity and the formation of black holes. This two-hour lecture, part of a broader course on neutron stars and black holes, offers a deep dive into astrophysics and provides a solid foundation for understanding these enigmatic cosmic phenomena.