The philosophy that guides the presentation is that though quantum theory does have a dynamical aspect, a predominant part of the theory is simply about a new kind of probabilistic model for expressing uncertainties of various kinds. [...] All the lectures in this book are presented in the author's characteristic no-nonsense style, making it a gem of a reference work. The bibliography, in fact, is a rich source of material, indispensable for filling in how to actually derive all the advertised results. The clear-cut purpose of the monograph is not to go through the mechanics of each theorem, but to paint a picture in modern art. Throughout, there is an emphasis on how each and every quantum result differs from its analog in the classical probabilistic model. One does, however, fear that a central illuminating thread is somehow missing from the exposition, though the author cannot be blamed: It is a thread no one has yet seen. [...] In the mean time, though, an exposition like this is part of the necessary journey. (Quantum Information and Computation 3/2, 2003)
The probabilistic structure of quantum theory has been investigated since the well-known monograph of J. von Neumann Mathematical Foundations of Quantum Mechanics [...]. The present book deals with the further development of the theory, namely with the modern consistent quantum statistical theory that was created in the 1970-80s as a logical extension of the statistical interpretation based on the mathematical foundation of modern functional analysis. [...] The book is written clearly and is self-contained. It will be useful for both mathematicians and physicists interested in the foundations of quantum mechanics. (Zentralblatt MATH, 999/24, 2002)
