London Mathematical Society Monographs. New Series. 28. Oxford: Oxford University Press. xiv, 395 p. £70.00 (2003).
28 years after its first appearence, Irving Reiner’s book “Maximal orders” has remained to be a standard reference to “non-commutative arithmetics”. Apart from the classical applications already mentioned in the book, there are some areas of currently active research, like non-commutative algebraic geometry or non-Abelian Iwasawa theory, where the theory of maximal orders has become an important requisite.
Not only for maximal orders, but also for general orders over a Dedekind domain, Reiner’s book provides an excellent introduction for students and serves as an indispensible reference for researchers. For a summary of contents we refer to the review Zbl 0305.16001 of the original.