The aim, both here and in Major Transitions, is not merely to describe the transitions, but to explain them, or at least provide speculations which could be explanatory. They make this more difficult --- but not unnecessarily difficult --- by insisting that the explanations conform to the canons of neo-Darwinism. That is, the transitions must be seen to be brought about by gradual changes, each of which is in itself adaptive for the organisms making the steps, or rather the genes which cause the organisms to make them. In other words: no cheating by looking ahead, no taking one step back to make two steps forward. Of course, each incremental advance needn't be adaptive for the same reason that the ultimate major transition is; "exaptations" (Gould and Vrba's useful term) are kosher. They are quite sound on why valid evolutionary explanations have to be of this form, and why, e.g., the otherwise-revered Lynn Margulis's idea that symbiosis can in itself explain adaptations is unacceptable.
In some cases (like the evolution of multicellularity), the trick is to make individual selfish replicators hang together (rather than separately). In that case, the trick is turned by imposing a reproductive bottle-neck: every cell in the body (pretty much) has the same set of genes, and all those genes have one route into the next generation, and equal chances of passing through it. It is this enforced community of interests that allows for coherent, adaptive development to evolve. (This argument was first put forward by John Tyler Bonner, and elaborated by Richard Dawkins.) In general, the ideas here about banding together are solid and convincing, which isn't too surprising, since we've been worrying over the evolution of association ever since ch. VII of On the Origin of Species. In the case of animal societies, we are fortunate to see many intermediate forms, ranging from completely solitary animals to ones which, like honeybees and human beings, are completely unable to survive and propagate outside of diversified social groups. (Maynard Smith and Szathmáry have a fine discussion of this process, with insect examples.)
Their ideas about the other class of transitions, the important shifts in the way replication happens, are less satisfying. It's not that Maynard Smith and Szathmáry are definitely wrong about anything; it's that they're flailing about in the twilight like everyone else. Of these troubling cases, the most troubling to my mind is the evolution of eukaryotes from prokaryotes. Eukaryotic cells (as found in ourselves, plants, slime molds and yeast) possess a distinct nucleus in which the chromosomes and related genetic apparatus reside, and numerous organelles, specialized organs within the cell, two kinds of which (mitochondria and chloroplasts) actually have their own DNA. Moreover, eukaryotes lack the rigid cell walls of prokaryotes (e.g. bacteria). Our authors plausibly portray the loss of the cell wall as the key innovation which made the others possible, but, unhappily, are unable to come up with any adaptive reason for it. For lack of a better idea, they fall back on the fact that prokaryotes produce chemicals which destroy the cell walls of their rivals; they suggest that we descend from something which was crippled but not killed by such an attack. The puzzles presented by the evolution of language are similar, but much less extreme, and here our authors are content to summarize the existing speculations, rather than advance any of their own. (They do not, however, mention William Calvin's idea, that grammar is an exaptation of neural machinery evolved for throwing.)
Major Transitions is reasonably technical, makes liberal use of biological jargon, and is full of details, not least on other people's ideas. For all that it, it is well-written: Maynard Smith was Haldane's disciple, and inherited not only the master's ability in mathematical biology, but his talent for writing clearly about complicated topics (and his socialist politics). The Origins of Life is a stripped-down version, simplified (e.g. omitting the more awful details of eukaryotic reproduction), schematic, less jargony, with some of the more speculative and/or lit.-review bits snipped. The only really annoying thing is that they've also omitted all the notes and references; to follow up on anything, you have to look up the corresponding section in Major Transitions, making that the (so to speak) developer's version. The Origins of Life is intended for intelligent non-biologists who want to get a handle on the Really Big Picture of the history of life, and I can't think of any better book for them.