Authors of popular science books are cautioned that each equation they include (except, perhaps E=mc˛) will halve the sales of their book. Penrose laughs in the face of such fears. In this “big damned fat square book” of 1050 pages of main text, there's an average of one equation per page, which, according to conventional wisdom should reduce readership by a factor of 2^{−1050} or 8.3×10^{−317}, so the single copy printed would have to be shared by among the 10^{80} elementary particles in the universe over an extremely long time. But, according to the Amazon sales ranking as of today, this book is number 71 in sales—go figure.
Don't deceive yourself; in committing to read this book you are making a substantial investment of time and brain power to master the underlying mathematical concepts and their application to physical theories. If you've noticed my reading being lighter than usual recently, both in terms of number of books and their intellectual level, it's because I've been chewing through this tome for last two and a half months and it's occupied my cerebral capacity to the exclusion of other works. But I do not regret for a second the time I've spent reading this work and working the exercises, and I will probably make a second pass through it in a couple of years to reinforce the mathematical toolset into my aging neurons. As an engineer whose formal instruction in mathematics ended with differential equations, I found chapters 12–15 to be the “hump”—after making it through them (assuming you've mastered their content), the rest of the book is much more physical and accessible. There's kind of a phase transition between the first part of the book and chapters 28–34. In the latter part of the book, Penrose gives free rein to his own view of fundamental physics, introducing his objective reduction of the quantum state function (OR) by gravity, twistor theory, and a deconstruction of string theory which may induce apoplexy in researchers engaged in that programme. But when discussing speculative theories, he takes pains to identify his own view when it differs from the consensus, and to caution the reader where his own scepticism is at variance with a widely accepted theory (such as cosmological inflation).
If you really want to understand contemporary physics at the level of professional practitioners, I cannot recommend this book too highly. After you've mastered this material, you should be able to read research reports in the General Relativity and Quantum Cosmology preprint archives like the folks who write and read them. Imagine if, instead of two or three hundred taxpayer funded specialists, four or five thousand self-educated people impassioned with figuring out how nature does it contributed every day to our unscrewing of the inscrutable. Why, they'll say it's a movement. And that's exactly what it will be.