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We live in this universe. Hence, it is essential to understand the origin, evolution and ultimate fate of the universe. This can be, effectively, done by constructing mathematical models of the universe, using Einstein's theory of gravitation and other modified theories of gravitation. The models, thus, obtained can be compared with the present day observations, to decide about the shape, physics, and origin of the universe. With this motivation we have taken up the investigations in this book entitled "STUDIES ON GRAVITATIONAL FIELD EQUATIONS AND IMPORTANT RESULTS OF RELATIVISTIC COSMOLOGY". This book comprises of six chapters and deals with some spatially homogeneous isotropic and anisotropic cosmological models of the universe in some modified theories of gravitation.