This thesis starts with the important discoveries of cosmology at 20th century and discusses the universe total density W and decelerating parameter q at different curvature k on the Friedman Model. By using qualitative analysis of the universal dynamic equations, we discuss the possible cosmological models with cosmological constant L . Beside using the three methods, the decay of heavy elements, the evolution of stars in the globular clusters, and the cooling of white dwarf , to get the lower limit age of the universe, we also use the latest observational data to get the lower limit of the universe. Then we describe the latest parameters of the universe in the present epoch and the evidences of the accelerating universe. According to the different cosmological models, we adapt the latest parameters to get the age of universe and compare the results with the observational data. Finally, it describes the two important experiments, SNAP and Planck, that will make the cosmology more accurate and precise in the future.