It's a delicate balance for book: Encyclopedic  vs well focused on a unifying theme!<br><br>  Penrose succeeds admirably. It's not boring! Books like this are few and far between. Indeed, there are preciously few authors who manage to successfully guide beginning students into serious scientific topics; and even fewer who can see the big picture, and do it all. And then keeping our attention through more than 1000 pages! Penrose's book is inspiring, informative, exciting; and at the same time it's honest about what math and physics are. It is modest when modesty is called for. You are not cheated. You do get the equations (not just hand waving!), but you are gently prepared in advance, so you will want the mathematical formulae. Penrose's book is likely to help high school students getting started in science; and to inspire and inform us all. There is something for everyone: for the beginning student in math or in physics, for the educated layman/woman (perhaps the students' parents), for graduate students, for teachers, for scientists, for researchers; and the list goes on.<br><br>It is one of the very few books of this scope that is not intimidating. Not in the least!<br><br>  I can't begin to do justice to this terrific book. Get it, and judge for yourself. I will also not give away the ending, other than saying that the title of the book is a good hint. And you will be able to form your own take, and your own ideas on the conclusion. Like with all good and subtle endings, they can be understood and appreciated at several levels.<br><br>  I came across Penrose's book in my bookstore by accident, and I was at first apprehensive: The more than 1000 pages, and the 3.3 pounds are enough to intimidate anyone. But when I started to read, I found myself unable to put it down. And I didn't: Bought it; and I had several days of enjoyable reading. I am not likely to put it away to collect dust either. It is the kind of book you will want to keep using, and to return to.<br><br>  It will not surprise that one of Penrose's unifying themes is the compelling and pleasing geometric images that underlie both the mathematics (roughly one third of the book: modern geometry, Riemann surfaces, complex functions, Fourier analysis, visions of infinity), and the physics: Cosmology (the big bang, black holes), gravity, thermodynamics, relativity (classical and modern: loop quantum gravity, twisters), and quantum theory (wave-particle duality, atomic spectra, coherence, measurements).<br><br>  The pictures: In fact, this semester, I was just teaching a graduate course, and I had a hard time presenting of Riemann surfaces in an attractive way. It's a subject that typically comes across as intimidating in many of the classical books: Take Herman Weyl's book, for example. I also found it refreshing to see that Roger Penrose gave the many illustrations his own personal and artistic touch; as opposed to having flashy pictures generated by the latest in color-graphics and special effects. I think readers will relate better to Penrose's own illustrations: They isolate and highlight the core ideas and they are not intimidating: We sense that we ourselves would have been able to make similar pencil sketches. Or at least we are encouraged to try!<br><br>  The common theme in the pictures serves to bring to life the underlying and fundamental ideas;--- another attractive feature of the book! It is otherwise easy to get lost in some of the equations, and in the encyclopedic panorama of topics.  Review by Palle Jorgensen, February 2005.