Peter Wakker is one of the most renowned theoretical researchers in the field of decision theory and particularly prospect theory. His axiomatization of cumulative prospect theory in a joint paper with Amos Tversky paved the way for Daniel Kahneman to win the Nobel Prize in Economics in 2002. Given this background, it is not a surprise that his book is a very thoughtful and in-depth overview of prospect theory. \par The first part of the book (on expected utility) begins with a discussion of basic decision-theoretical concepts, e.g.\ the expected value and the no-arbitrage condition. It continues with an explanation of the expected utility approach, where the author includes the case of decisions under risk in the more general framework of decisions under uncertainty. In this part, many interesting applications are given and some original theoretical connections are drawn. Already this makes the first part of the book, which one might otherwise expect to only repeat introductory material that is available elsewhere, a very interesting and refreshing source of classical and recent results on expected utility theory. Although the author is foremost a theoretician, there are also many problems discussed that are important for empirical research in this area, e.g.\ how to fit experimental data to expected utility under risk or under uncertainty. \par In the second part of the book (non-expected utility for risk) he discusses in detail rank-dependent utility and then prospect theory. There are many interesting points mentioned here that are far from being standard material, but are nevertheless very important, e.g.\ Rabin's paradox, and they give convincing theoretical-empirical reasons against the empirical validity of expected utility theory. \par However, one thing to keep in mind about this part (and what follows) is that when the author talks about ``prospect theory'' he actually means what in academia is usually called ``cumulative prospect theory''. The original formulation of prospect theory, going back to the well-known article by Kahneman and Tversky from the year 1979, is only mentioned in an appendix of the second part and is not really discussed in detail, because it lacks some theoretically desirable properties. Given the empirical evidence in favor of the original formulation of prospect theory, this may be a minor gap in the book. \par In the third part, the author discusses non-expected utility under uncertainty. His main idea is to extend the already established concepts from decisions under risk to situations of uncertainty, i.e.\ where probabilities are not known. He starts with extending the concept of rank-dependent utility to uncertainty and then later goes on to prospect theory. In this part, many different approaches to decisions under uncertainty are discussed, and also the classical motivation to this problem, the Ellsberg paradox, is discussed in detail. \par The book presents in all its parts a very deep and solid theoretical introduction to decision theory under risk and uncertainty, not only prospect theory. In this sense, it provides more than its title suggests. \par While the mathematical formalism of this book is substantial (not so much for mathematicians, but definitely for readers from other fields like economics), it is always (at least with some effort) readable, and the many examples, illustrations and applications motivate the reader well and illustrate the concepts in a very efficient manner. The book not only can be used on an advanced level as material for a seminar in economics (according to my experience at least), but can also be used as a rich resource for researchers in this field, since it definitely reaches its goal of providing a complete overview of all aspects of prospect theory and related decision-theoretical models.