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Teams of prominent American and European Scientists using both Hubble Space Telescope and Earth based Telescopes had announced in 1998 by Type Ia supernovae observation that the Universe is not just expanding, it is in fact, expanding with ever increasing speed. This combined discovery has been a total surprise for Cosmology! This physical feature is caused by the term dark energy . The implosion of a star or other celestial body as a result of its own gravity, results in a body that is many times smaller and denser than the original body. The physical process under the influence of gravity may form in naked singularity or black hole. The accelerating models and gravitational collapse models are the hot topics of current research in the twentieth century. The purpose of this book is to present a study on Relativity and Cosmology for the university students who are pursuing this line of research. The contents of this book should especially encourage the researchers, Physicists andMathematicians involved in the in-depth study of Accelerating Models of the Universe and Gravitational Collapse.