Classification of cosmological models in Einstein's general theory of gravity.

In this thesis, I first review the fundamentals of Hot Big Bang cosmology, the observational cosmology and the late accelerating universe. Then I systematically study the evolution of the Friedmann-Robertson-Walker (FRW) universe with a cosmological constant Λ and a perfect fluid that has the equation of state p=wρ, and classify all the solutions into various cases, where p and ρ are the pressure and energy density of the fluid, and w is a constant. In each case the main properties of the evolution of the universe are studied in detail, including the periods of deceleration or acceleration, and the existence of big bang, big crunch, and big rip singularities. Finally, I mention some future work along the direction laid down in this thesis.