This concise and comprehensive treatment of the basic theory of algebraic Riccati equations describes the classical as well as the more advanced algorithms for their solution in a manner that is accessible to both practitioners and scholars. It is the first book in which nonsymmetric algebraic Riccati equations are treated in a clear and systematic way. Some proofs of theoretical results are simplified and a unified notation is adopted. The book includes a unified discussion of doubling algorithms and a detailed description of all classical and advanced algorithms for solving algebraic Riccati equations and their MATLAB(r) codes. This will help the reader to gain an understanding of the computational issues and provide ready-to-use implementation of the different solution techniques. Ideal for researchers working in the design and analysis of algorithms and for practitioners who need to understand the available algorithms and software.