Regulator; IV. Extensions to More Complex Problems; and V. Computational Aspects. Two appendices in Matrix and System Theory are presented. Glancing over the chapter headings will confirm what the parts' titles indicate: this is not a book on system theory; neither is it a book on optimization theory, in general. As a matter of fact, it is not even a book on optimal control theory for linear systems. However, in spite of the above statements, Anderson and Moore's Linear Optimal Control is perhaps the best introduction to optimal control theory available today. This is true for several reasons. The book covers an important part of control theory, namely, Linear Optimal Control Theory; it relates optimal control theory to classical control theory; it extends results of linear optimd systems to some important but specific nonlinear systems; and by restricting the mathematical derivation to the use of the Hamilton-Jacoby Theory, it is reasonably self-contained. There is also the need for a second course on optimization methods for those interested in optimal control; this second course might either stress the mathematical aspects of optimization or emphesize other techniques and problems in optimal control. The books by Athans and Falb (1) and by Sage (2) might serve for those purposes, respectively. Briefly reviewing the core of the book, Part II deals with the basic theoretical aspects of the optimal regulator, using the Hamilton-Jacoby theory as the mathematical tool. In spite of the fact of being sometimes hard to follow, it is well written and concise. Part III deals with several applications and properties of the optimal regulator, including its relationship with classical theory, insertion of nonlinearities, sensitivity aspects and state estimation. It unquestionably gives the student comprehension of the material that can only come through applications. Part IV follows with more extensions and applicetions to problems with input disturbances, tracking systems, controller constraints, dual mode control and special topics in discrete and time-varying systems. Part V on computational aspects deals with the solution of the Riccati equation. As such