This book reviews in a unified manner global aspects in gravitation theory and cosmology, emphasizing the basic heme that the very nature of the gravitational field is such that global features of space-time inevitably come into play whenever we try to understand and interpret this force in detail. The topics considered here include results on the structure and topology of space-time; exact solutions to Einstein equations and singularities ; gravitational collapse in general relativity, a brief review of the status of quantum gravity; and consideration of quantum effects near space-time singularities in strong curvature fields. Also covered are the global upper limits in cosmology on elementary particle masses which might constitute the dark matter of the universe. After discussing in detail the fundamental role played by global considerations in gravity and general relativity, it is pointed out that significant problems remain: the nature and structure of space-time singularities; the cosmic censorship problem in black hole physics; and the issue of quantum effects in strong gravity fields, an understanding of which appears essential to formulate any quantum theory of gravity. The treatment here of the final fate of gravitational collapse of massive stars shows by means of explicit consideration of several exact scenarios, that powerfully-strong curvature naked singularities could result from the continual gravitational collapse of matter with several reasonable equations of state, including inflowing radiation, dust, or a perfect fluid. This places important constraints on possible formulations of the cosmic censorship hypothesis and the final fate of gravitational collapse, which is a crucial open question in the general theory of relativity and relativistic astrophysics and which is basic to the entire theory and applications of black hole physics.