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Curvature Cosmology proposes a new cosmological model very different from, and more elegant than, the Big-Bang Theory. Curvature Cosmology is based on two major hypotheses that Hubble redshift is due to an interaction of photons with curved spacetime and that there is a pressure that acts to stabilise expansion and provides a static stable universe. The main focus of this book is to describe these two hypotheses in detail and to examine all relevant cosmological data in the context of this new model of the universe. This model proposes that, though evolution of stars and galaxies is evident, the statistical properties of the universe are the same at all places and at all times. In short, the universe is ageless, has no defined beginning (unlike the Big-Bang model), and carries no evidence of expansion, despite the changeability of its components. Curvature Cosmology is a complex book that calls for a paradigm shift in current cosmology and requires at least basic (if not more complex) knowledge of past and current cosmological models and equations.