As the title of this book suggests, it is aimed primarily at researchers working on a rather specific area: the Hamiltonian quantization of minisuperspace models arising from supergravity theories. The book gives a thorough summary of this field, and provides a clear introduction for a graduate student. For a more general audience, the first few chapters of the book could serve as a basic reference for the fundamentals of canonical quantum gravity and quantum cosmology.

The first three chapters of this book are likely to be the most useful to the average reader, since they deal with the rudiments of the canonical quantization of general relativity and supergravity. The presentation of these early chapters is good with a pedagogical style that makes the mathematics easy to follow, and an extensive bibliography that covers most of the principal results in quantum cosmology. The treatment of the canonical quantization of supergravity in Chapter 3 is relatively clear, provided the reader is comfortable with Weyl spinor notation.

Before recommending the first half of the book too enthusiastically as an introduction to canonical quantum gravity, I should point out that there is relatively little attempt to put canonical methods into context as a method for quantizing general relativity. In this sense, the author probably places too much emphasis on mathematical results and on summarizing a particular literature, without tackling broader motivational questions. I should also mention that the review contains some specific omissions, such as a description of Vilenkin's proposal for the wavefunction of the Universe.

Chapters 4 to 7 appear to be clearly written, but will be of interest to a small number of researchers. Chapter 4 deals with semiclassical expansion of the quantum wavefunction and the two-loop finiteness of supergravity. Chapters 5 and 6 summarize results for minisuperspace models of quantum supergravity, a number of which have been solved exactly. It is a shame that the book was written too early to include some recent results due to Graham and collaborators. Chapter 7 describes the use of Ashtekar variables in supergravity, and gives a useful summary of some rather pretty simplifications that arise when using these new variables.

The book ends with a couple of chapters containing some of the author's speculations and conclusions. Some of this material is rather controversial, but it is hard for me to give an objective opinion since I am a coauthor of a paper that takes an opposite position. Perhaps these last few sections would therefore be better suited to a research journal, but some readers may find them of interest.