This is a splendidly written book, one of a number by three of the world's leading linear algebraists, that collects many results on indefinite linear algebra from the literature and puts them all in a single place. The book is based in part on a 1983 book titled Matrices and Indefinite Scalar Products by the same authors and publisher but includes many contemporary results from the journal literature and elsewhere. In fact, the ends of many of the chapters provide a guide to sources where further materials are to be found. There are some excellent exercises collected at the end of each chapter making the book ideal as a graduate-level textbook. (SIAM Review) "The reviewer is convinced that the present book will be welcome by all readers interested in applications of indefinite linear algebra in matrix polynomials, differential equations and difference equations with constant coefficients." Mircea Crasmareanu, Analele Stiintifice

• and Outline.- Indefinite Inner Products.- Orthogonalization and Orthogonal Polynomials.- Classes of Linear Transformations.- Canonical Forms.- Real H-Selfadjoint Matrices.- Functions of H-Selfadjoint Matrices.- H-Normal Matrices.- General Perturbations. Stability of Diagonalizable Matrices.- Definite Invariant Subspaces.- Differential Equations of First Order.- Matrix Polynomials.- Differential and Difference Equations of Higher Order.- Algebraic Riccati Equations.