Did time begin? Will time end?

Did time begin at a Big Bang? Will the present expansion of the universe last for a finite or infinite time? These questions sound philosophical but are becoming, now in the twenty-first century, central to the scientific study of cosmology. The answers, which should become clarified in the next decade or two, could have profound implications for how we see our own role in the universe. Since the original publication of Stephen Hawking's {\it A Brief History of Time} in 1988, the answers to these questions have progressed as a result of research by the community of active theoretical physicists including myself. To present the underlying ideas requires discussion of a wide range of topics in cosmology, especially the make up of the energy content of the universe. A brief summary of my conclusions, that of three different possibilities concerning the history and future of time, the least likely is the conventional wisdom (time began and will never end) and most likely is a cyclic model (time never begins or ends), is in the short final Chapter which could be read first. To understand the reasoning leading to my conclusions could encourage reading of my entire book. My hope in writing this, my first popular book, is that it will engender reflection about time. Many a non-scientist may already hold a philosophical opinion about whether time begins and ends. This book's aim is to present some recently discovered scientific facts which can focus the reader's consideration of the two short questions in my title.