Avner Ash is Professor in the Department of Mathematics at Boston College, Massachusetts. David Mumford is Professor Emeritus of Applied Mathematics at Brown University, Rhode Island. Michael Rapoport is Professor in the Mathematical Institute of the University of Bonn, Germany. Yung-sheng Tai is Associate Professor of Mathematics at Haverford College, Pennsylvania.

• Preface to the second edition; Preface to the first edition; 1. Basics on torus embeddings: examples; 2. Polyhedral reduction theory in self-adjoint cones; 3. Compactifications of locally symmetric varieties; 4. Further developments; Supplementary bibliography; Index.

'The book under review is a new edition of the authors' celebrated research monograph … which must be seen as one of the milestones in contemporary algebraic and complex-analytic geometry … No doubt, this classic will maintain its outstanding role in algebraic geometry, Hermitian differential geometry, group representation theory, and arithmetic geometry also in the future, especially for active researchers and graduate students in these related areas of contemporary pure mathematics. In this regard, the present new edition of it is certainly more than welcome.' Zentralblatt MATH