The problem with many popular science books is that they limit themselves to working within the bounds of scientific consensus, and eliminate any mathematical technicalities for the benefit of the reader. Though Brian Greene's book moves the maths discreetly to an endnotes section, he does give pointers for more technically inclined readers, and he isn't afraid to say that much of the work of string theory is speculative and not well understood.
After an introduction, the book begins with a chapter each on special relativity, general relativity and quantum mechanics. The two chapters on Einstein's relativity theories are excellent - some of the ideas presented about special relativity, such as the idea that everything is continuously moving through spacetime at constant speed (it's just that you and I move almost entirely through time, whereas a photon moves entirely through space), I could have done with when I was studying it at university. The chapter on quantum mechanics is fair enough, but perhaps a bit muddled for someone who knows a bit about the subject. It's very tempting to read explanations of the Uncertainty principle as limitations on our measurement apparatus, rather than an intrinsic limitation that, on the quantum scale, particles do not have well-defined position and momentum.
Going on to describe the main principles of string theory, Greene entertains us with the Kaluza-Klein extension of general relativity before introducing 10-dimensional Calabi-Yau spaces. I won't pretend to understand the detail, but Greene's "in principle" explanations are usually well-formed analogies that can be understood by anyone with a logical and enquiring mind. He doesn't deny the speculative nature of the theory, and accepts the controversy and lack of clear experiments that could be performed to test pre- or post-dictions of the theory. Nevertheless, he is able to offer convincing qualitative explanations of things such as the number of elementary particle families.
The heaviest section of the book deals with quantum geometry and M-theory. Even without the mathematics, these chapters are quite technical, though Greene lightens them in part by switching to an autobiographical mode, describing in personal terms the progress of his research with others in the field. The chapter on Black Holes is, again, qualitatively convincing.
A weakness in the book (and perhaps in the theory) is that the Uncertainty principle is used in many ways as a starting point: to be a truly satisfying theory, I would prefer the Uncertainty principle to emerge from the theory. Perhaps I am inconsistent here, as I have no problem with special relativity, which uses the constancy of the speed of light as one of its postulates (This was experimentally verified to high accuracy before the theory, but it contradicted the common-sense expectations of scientists who believed light should travel through an "aether", and therefore its observed speed should fluctuate based on relative motion between sender and receiver. The verification of quantum mechanical predictions arguably validates the Uncertainty principle in the same way, but to me the Uncertainty principle is reminiscent of Ptolemaic epicycles to explain planetary motion).
Greene's concluding chapter verges on metaphysics: do space and time actually exist, is there an ultimate theory, and so on. It's interesting to me that (even in Hofstadter's Godel, Escher, Bach) I have never seen a discussion of Godel's undecidability theorem with respect to the "Theory of Everything". If the Universe is a Formal System, it must be incomplete. Nevertheless, Greene has demonstrated that he is a talented and courageous writer for presenting the material in an intelligent but accessible way.