Over the last century, the investigations in Gravitation and Cosmology have attracted the attention of thousand of human minds. Apart this boom in popularity, the homework task for cosmologists is to try to give an answer to the reasons why the present Universe has the properties that are observed. In spite of having a well-established theoretical framework like the Einstein's gravity theory (GR), which is valid in an amplest rank of energies and that has responded satisfactorily to numerous empirical verifications, are numerous unanswered intriguing questions. Is the dark energy the cause of the acceleration of the expansion? What is its equation of state nowadays? Why the energy densities of matter and dark energy of the same order of magnitude nowadays? Will be the acceleration of the expansion an indication that the action of Einstein-Hilbert must be modified? Can be reached the isotropic degree of the universe that is observed today, independently of the initial degree of anisotropy? In this book are studied, from the perspective of the dynamical systems, several Universe models that try to give answers to some of these questions.