Although everyone is familiar with the concept of time in everyday life and has probably given thought to the question of how time began, latest scientific developments in this field have not been accessible in a simple understandable form. This book is important as it presents to readers current ideas about the role of time in theoretical cosmology. Recent observational discoveries, especially that the expansion rate of the universe is accelerating, have revolutionized the understanding of the energy content of the universe (only a small fraction of about four percent is normal matter; the remainder is about twenty-four percent dark matter and seventy-two percent dark energy). Thus the dark side of the universe, especially dark energy, leads to new possibilities for the beginning and end of the universe. This book emphasizes the notion of entropy and describes how it is theoretically possible that the universe may end in a finite time. Although this book does not provide definitive answers to the questions posed in the title, it provides 21st century scientific knowledge, written by a leading theoretical physicist, that will better enable an informed reader to discuss the nature of time.