  In this book are studied, from the perspective of the dynamical systems,
several Universe models. In chapter 1 we give a bird's eye view on cosmology
and cosmological problems. Chapter 2 is devoted to a brief review on some
results and useful tools from the qualitative theory of dynamical systems. They
provide the theoretical basis for the qualitative study of concrete
cosmological models. Chapters 1 and 2 are a review of well-known results.
Chapters 3, 4, 5 and 6 are devoted to our main results. In these chapters are
extended and settled in a substantially different, more strict mathematical
language, several results obtained by one of us in arXiv:0812.1013 [gr-qc];
arXiv:1009.0689 [gr-qc]; arXiv:0904.1577[gr-qc]; and arXiv:0909.3571 [hep-th].
In chapter 6, we provide a different approach to the subject discussed in
astro-ph/0503478. Additionally, we perform a Poincar\'e compactification
process allowing to construct a global phase space containing all the
cosmological information in both finite and infinite regions for all the
models.
