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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 have been simplified and a unified notation has been adopted. Readers will find a discussion of doubling algorithms, which are effective in solving algebraic Riccati equations, and a detailed description of all classical and advanced algorithms for solving algebraic Riccati equations, along with their MATLAB® codes. This will help the reader gain understanding of the computational issues and provide ready-to-use implementation of the different solution techniques.