The book "Representation and Control of Infinite Dimensional Systems" is a comprehensive reference on the control of infinite dimensional systems, covering both theoretical and practical aspects. It is divided into five parts, each focusing on different aspects of control theory. Part I provides an overview of finite dimensional linear systems and introduces the concept of linear quadratic two-person zero-sum differential games. It discusses controllability, observability, stabilizability, and detectability, and includes a new chapter on the theory of dissipative systems. Part II deals with the representation of infinite dimensional systems, including semigroup theory, variational methods, and the representation of dynamical partial differential equations. Part III examines the qualitative properties of controlled systems, including controllability and observability for infinite dimensional systems. Part IV and Part V present a dynamical programming approach to the optimal linear quadratic control problem over finite and infinite time horizons, respectively. The book also includes a detailed discussion of the Riccati differential equation and its role in optimal control. The second edition of the book has been revised and corrected, with an expanded scope and integrated bibliography. The authors acknowledge the support of various institutions and individuals in the development of the book. The book is intended for researchers and advanced engineers in the field of systems and control.The book "Representation and Control of Infinite Dimensional Systems" is a comprehensive reference on the control of infinite dimensional systems, covering both theoretical and practical aspects. It is divided into five parts, each focusing on different aspects of control theory. Part I provides an overview of finite dimensional linear systems and introduces the concept of linear quadratic two-person zero-sum differential games. It discusses controllability, observability, stabilizability, and detectability, and includes a new chapter on the theory of dissipative systems. Part II deals with the representation of infinite dimensional systems, including semigroup theory, variational methods, and the representation of dynamical partial differential equations. Part III examines the qualitative properties of controlled systems, including controllability and observability for infinite dimensional systems. Part IV and Part V present a dynamical programming approach to the optimal linear quadratic control problem over finite and infinite time horizons, respectively. The book also includes a detailed discussion of the Riccati differential equation and its role in optimal control. The second edition of the book has been revised and corrected, with an expanded scope and integrated bibliography. The authors acknowledge the support of various institutions and individuals in the development of the book. The book is intended for researchers and advanced engineers in the field of systems and control.