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INTRODUCTIONThis collection of papers reflects the problems that I have worked on over the years. With hindsight, it might appear that there had been a grand and premeditated design to address the outstanding problems concerning the origin and evolution of the universe. But it was not really like that. I did not have a master plan; rather I followed my nose and did whatever looked interesting and possible at the time.There has been a great change in the status of general relativity and cosmology in the last thirty years. When I began research in the Department of AppUed Mathematics and Theoretical Physics (DAMTP) at Cambridge in 1962, general relativity was regarded as a beautiful but impossibly complicated theory that had practically no contact with the real world. Cosmology was thought of as a pseudo-science where wild speculation was unconstrained by any possible observations. That their standing today is very different is partly due to the great expansion in the range of observations made possible by modern technology. But it is also because we have made tremendous progress on the theoretical side, and this is where I can claim to have made a modest contribution.Before 1960, nearly all work on general relativity had been concerned with solving the Einstein equations in particular coordinate systems. One imposed enough symmetry assumptions to reduce the field equations either to ordinary differential equations or to the Laplacian in three dimensions. It was regarded as a great achievement to find any closed form solution of the Einstein equations. Whether it had any physical significance was a secondary consideration. However a more geometric approach began to appear in the early 1960s in the work of Roger Penrose and others. Penrose introduced global concepts and showed how they could be used to establish results about spacetime singularities that did not depend on any exact symmetries or details of the matter content of the universe. I extended Penrose's methods and applied them to cosmology. This phase of work on global properties came to an end in about 1972 when we had solved most of the qualitative problems in classical general relativity. The major problem that remains outstanding is the Cosmic Censorship Conjecture. This is very difficult to prove, but aU attempts to find genuine counter-examples have failed, so it is probably true.This global classical phase of my work is represented by the first three papers in this volume. They deal with the classical properties of the two themes that recur throughout my work: the Big Bang and black holes. Nowadays everyone accepts it as natural that the universe had a beginning about 15 billion years ago and that, before that, time simply was not defined. But opinions were very different in the early 1960s. The Steady State school believed that the universe had existed forever more or less as we see it today. Even among those who thought the universe was evolving with time, there was a general feeling that one could not extrapolate back to the extreme conditions near the initial singularity of the Friedmann models and that it was probably just an artifact of the high degree of symmetry of these solutions. Indeed in 1963 Lifshitz and Khalatnikov claimed to have shown that singularities