General Theory.- Rickart ?-Rings, Baer ?-Rings, AW*-algebras: Generalities and Examples.- Comparability of Projections.- Structure Theory.- Structure Theory of Baer ?-Rings.- Additivity of Equivalence.- Ideals and Projections.- Finite Rings.- Dimension in Finite Baer ?-Rings.- Reduction of Finite Baer ?-Rings.- The Regular Ring of a Finite Baer ?-Ring.- Matrix Rings over Baer ?-Rings.- Errata and Comments for Baer ?-Rings.- Errata and Comments for Baer ?-Rings.

A systematic exposition of Baer *-Rings, with emphasis on the ring-theoretic and lattice-theoretic foundations of von Neumann algebras. Equivalence of projections, decompositio into types; connections with AW*-algebras, *-regular rings, continuous geometries. Special topics include the theory of finite Baer *-rings (dimension theory, reduction theory, embedding in *-regular rings) and matrix rings over Baer *-rings. Written to be used as a textbook as well as a reference, the book includes more than 400 exercises, accompanied by notes, hints, and references to the literature. Errata and comments from the author have been added at the end of the present reprint (2nd printing 2010).