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This thesis titled "Certain Studies on Dark Energy Cosmological Models in Einstein and Alternative Theories of Gravitation" is devoted to the investigation of some spatially homogeneous and anisotropic dark energy cosmological models in Einstein's general theory of relativity and alternative theories of gravitations: Brans-Dicke (1961) and S¿aez-Ballester (1986) scalar-tensor theories of gravitation, f(R) (Capozziello 2002; Nojiri and Odintsov 2007a) and f(R, T) (Harko et al. 2011) modified theories of gravitation. A cosmological model is a mathematical representation of the universe at some averaging scale. It describes the geometry of space-time, the distribution and properties of matter in the universe within the framework of some physical theories (commonly Einstein's and alternative theories of gravitation