This is a beautiful review. It is clear on technical issues; it is very critical, albeit respectful. It is informative to experts and non-experts alike; the formal apparatus is used to provide clarity not to create an esoteric, gated garden. It calls attention to unexplored alternative positions, and does so not just to keep scholarly score, but especially in order to illuminate the philosophical possibility space. It also contains a touch of wicked humor. (I return to that below.)
Note that Takashi Yagisawa (the reviewer) does not offer a detailed summary of the book; it is, thus, not balanced. Readers have to trust his judgment that he has focused on the central issues that are relevant to the community. Only competent readers of the whole book can decide, thus, if the review is fair. For some, the lack of summary may be a fatal flaw. Such people think that the main duty of a review is to tell people what's in a book. While that is important (which is why judicious summaries are often part of great reviews), it need not trump other considerations of the sort mentioned in the first paragraph.
I close with the wicked humor:
Its main goal is to argue for a metaphysical claim, necessitism, by taking modal logic seriously. Necessitism says that necessarily everything is such that necessarily it is identical with something. In the possible-worlds framework, this means that for any possible world w, anything existing at w is such that for any possible world w' it is identical with something existing at w'. That is, anything that exists anywhere in logical space exists everywhere in logical space; every possible thing is a necessary thing. This is an extremely radical claim -- as radical as David Lewis's modal realism, perhaps even more so. Just as Lewis attempted to provide correspondingly strong arguments in favor of his radical thesis (Lewis 1986), Williamson attempts to give appropriately strong evidence for his radical claim. Lewis was clear, meticulous, and ingenious in his attempt. Williamson is equally clear, meticulous, and ingenious in his attempt, and just as convincing as Lewis was.