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Many who wish to buy this book will be familiar with the other works of Professor Roger Penrose (such as The Road to Reality). Some will be curious to learn about a new theory of the origin of the Universe. This book presents a radical new idea which Penrose has been developing in the past few years on the Big Bang: essentially the idea is that there was a pre-Big Bang era and there will be a post-Big Crunch era too. So one could review both the book and the idea itself. Firstly some will worry about the level of mathematics presented in this book. In the main chapters there are equations such as S = k log V - Boltzmann's Equation. If you are not comfortable with this, then maybe you will not get the most from the book. However if you are comfortable with this and similar physics equations and numbers then the first section of the book is readable. Of course there are plenty of diagrams too. There is some hard maths however and this has been relegated to the Appendix (30 pages). This maths is very advanced and another of Penrose's technical books (Penrose and Rindler Volume 2) would be needed to understand it fully - so that is only for the experts. Given that the reader wont be learning this material in the present book it shows that there is some more complex machinery behind the scenes needed to comprehend the full idea. In the first section the book returns to an old concern of Penrose namely the entropy present in the early universe: less than today - but why so much less? The chapter then focusses in on the Big Bang described using "Conformal Diagrams". The key on page 115 is important for reading these diagrams. Part 3 introduces the new idea called Conformal Cyclic Cosmology (CCC). Here we learn something about the idea that the Big Bang is merely a transition in the longer history of the universe. To get the most out of the mathematics in this section one needs to understand the idea of the conformal metrics introduced. Fortunately there are no calculations about it in the main text, but the idea needs to be understood. In order to develop the CCC hypothesis Penrose then needs to consider various physics issues: entropy, black hole information loss, the presence of mass in elementary particles. A novel use of other work in these areas provides for an interesting basis for the CCC hypothesis as we also study the far future of the Universe. Finally we close with some observational details from the Cosmic Background Data being gathered by satellites. So CCC is a physically testable theory! If you are interested in another theory being presented at the forefront of Cosmology and Physics then this is for you. Also it provides another view of Penrose's approach to these subjects which is different from the mainstream. But beware that some of the mathematical ideas (of conformal infinity) go quite deep indeed - easily the subject of another book if this idea is successful!