The author of this book is well known to those who have studied general relativity and its quantization, his contributions to these areas going back to the 1960's. Indeed, the (black hole) singularity theorems and the invention of twistor theory are both credited to the author. The first of these is straightforward to learn from a mathematical standpoint, while the second can be very difficult to assimilate, as it is typically not motivated very well in the research literature. The author does discuss twistor theory in the book, but the discussion is not well motivated, and will be very disappointing to those readers who were expecting one that would be intuitively clear.<br><br>However, there are many places in the book where the author gives the reader special insight. Some of the these discussions include: 1. The discussion of the axiom of choice and the Banach-Tarski theorem, revealing the non-constructive nature of the latter, and also revealing the author's Platonism. Clearly the author does not favor a purely constructive approach to mathematics. Such an approach though would not only serve mathematics better but also its physical applications. Bizarre and counterintuitive results such as the Banach-Tarski theorem, incompleteness theorems, and non-computability results that arise from Cantor diagonalization would disappear, as they should, since they have no practical or observable consequences. 2. The treatment of complex numbers is thorough, but unfortunately the author has christened them as "magical." This reinforces the view that complex numbers have some of special or mystical status in mathematics, which they do not. In addition, their use in physical applications is not mysterious either in spite of their not being used for such for 350 years after their invention in 1545. 3. The discussion on analytic continuation, which is presented in a way which will make the transition to sheaf theory much more palatable. Indeed the author describes the existence of complex smoothness in an open region in the complex plane as being equivalent to the existence of a power series expansion about any point in this region. Thus a holomorphic function is one which can be analytically continued about a sequence of points. The author refers to this as a `rigidity' of holomorphicity, in that once a holomorphic function is fixed in its original region, and the path is fixed, the function can only be extended in one way. Real-analytic functions do not have this special property. 4. The discussion of quantum entanglement and quantum teleportation is very clear, with the only minus being that the author is too accepting of the reality of entanglement, and does not review critically the experimental evidence for this phenomena. A highly critical analysis of entanglement has not been done in the literature, even though such an analysis is sorely needed, due to the importance of entanglement as a mechanism to make quantum computation a reality. 5. The author mentions briefly an extension of the standard model that involves associating to each non-Abelian symmetry group a dual group, which is the same (abstract) group but will typically be broken. Most interestingly, this procedure results in a theory that only has three adjustable parameters, which definitely makes it reasonable to describe it as a significant advance in mathematical physics. 6. The chapter on the Big Bang and its "thermodynamic legacy" is the best in the book, for it addresses issues in a way that is both easily understandable and mathematically sound. The author presents the Big Bang as being "extraordinarily special" due to its low (relatively speaking) entropy. His discussion leads him into considerations of the anthropic principle, and he refreshingly recommends caution in giving this principle a religious interpretation. The author follows this by a fascinating discussion that reveals just how weak the anthropic principle is, and he once again expresses preference for naturalistic explanations on explaining the special nature of the Big Bang.