Cosmology is the study of the largest scale structure of the universe. Cosmology seeks to understand the nature of the universe, as well as, its origin, evolution, fate, structure, and its laws. The universe is not simply a random collection of irregularly distributed matter, but it is a single entity; all parts of which are in some sense is the unison with all other parts, and the laws of physics are the same everywhere. In this book we have tried to describe global structure of gravitation theory and cosmology, and the space-time singularities in the light of Einstein equations. Here we stress on two remarkable predictions about the universe: i) the final fate of massive stars is to collapse behind an event horizon to form a black hole which will contain a singularity, and ii) there is a singularity in our past is called big bang, a beginning of the universe. In both of the cases the curvatures and densities could be infinite. The occurrence of these singularities indicates incompleteness in the theory of space-time manifold. Global upper limit of the age of the universe is prepared on the basis of Friedmann models.
