In the preface to this book, the author writes that he set out with the desire to write a popular book along the lines of A Brief History of Time but on the subject of evolution. He soon recognized that the book "refused to be written that way" and became much more scientific and specialized. This is quite true. I am not a biologist but a physician, so I have had a fair number of biology courses, but much of this book was at about the limit of my ability to absorb, or even beyond. You probably won't get very far without a basic understanding of molecular biology: chromosomes, genes, DNA, tRNA, mRNA, transcription, translation, replication, ribosomes, operons, introns, splicing, and so on. On the other hand, if you have that background and some basic understanding with the concepts of biological evolution, you'll probably do fine with the book; little else is required--no math or biochemistry, for example. So be sure to take advantage of the "Look Inside" feature before you buy.
It's important to note the subtitle, "The Nature and Origin of Biological Evolution." This is not a chronicle of evolution, but a rather detailed (for a layperson) look at mechanisms of evolution, mostly at the genetic level, along with some reasoning and speculation about how the whole ball of wax got started.
You should also be aware that the "highest" organisms considered in any detail are the earliest, single-cell eukaryotes. Animals are, after all, only "a single, relatively small, tight group of eukaryotes" while bacteria and viruses are the most numerous and successful organisms on earth. Virtually the entire book is based on the evolution of bacteria, archaea, and viruses, though occasionally animals and plants are mentioned in passing. This is fine, since the purpose of the book is to explore evolution beyond the classical understanding of natural-selection-based, adaptive evolution, and also to probe the earliest origins of life.
I'm not sure what previous reviewer Jim means by "But it will be a classic because it deals handily with nearly every contested area of evolution, neatly demolishing every criticism leveled by creationists. It does this by making positive statements about what is known rather than by arguing against creationism." The book certainly deals with some contested areas, but the contests are among evolutionary biologists and not between creationists and biologists. This book and creationists are not in the same universe of discourse.
A few of the book's interesting points include:
* At least at the "interesting" scale of evolution (up to the origin of eukaryotes), adaptation or positive natural selection is not the major factor in genetic change: "the overall quantifiable characteristics of genome architecture, functioning and evolution are primarily determined by non-adaptive, stochastic processes. Adaptations only modulate these processes."
* Increasing complexity over time is not a measure of some kind of "progress" of evolution, but is due largely to two factors: (1) a random-walk phenomenon in which more complex structures will occur by chance given longer periods of time (2) the natural result when the effective population size is not great enough for purifying selection to eliminate slightly deleterious mutations. "Junk" DNA can accumulate as a result, both requiring and providing the substrate for complexity. Complexity as a "syndrome" of less-numerically-successful lineages coping with junk.
* Viruses as a separate "empire" of life not as a derivative of cellular life. The important role of viruses (and other conceptually-related entities) in evolution especially through horizontal gene transfer.
* The importance of the "Red Queen" arms-race between hosts and parasites (including especially viruses and other selfish elements) in driving genetic change.
* The logical necessity of an "RNA world" as precursor of cellular life. At the same time, the extreme improbability of the whole replication system arising in this universe: a "back of envelope" estimate of the probability of life evolving somewhere in the observable universe in 10 billion years is something like one in 10 to the power 1000. The author resorts to the "many worlds in one" hypothesis in which there are an infinity of infinite universes, so every possible event happens in not only one but an infinite number of them. We're here to observe one of these extremely improbable universes only because, of all these universes, living observers can only exist in the ones where life did arise ("weak anthropic principle").