Today, the accelerated expansion of the universe is a controversial subject, and the theories put forward to explain it vary widely. Some of these theories involve the correction of Einstein’s field equations and in others an unknown component known as dark energy responsible for accelerating expansion of the universe. In the early parts of this thesis, we have introduced a method called Applied cosmography, and we have examined some models of cosmology without dark energy. Then we introduce the dynamical systems method and apply it to two different models, one in which dark energy is present and in other the dark energy is absent. In the final sections of this thesis, we study the thermodynamic laws of dark energy with the constant equation of state parameter and with variable equation of state parameter and obtain the thermodynamic stability conditions of the universe for each of these states separately. Finally, we examine the possibility of thermodynamic stability in future singularities.