This monograph presents a detailed and unified treatment of the theory of reduced order systems. Covered topics include reduced order modeling, reduced order estimation, reduced order control, and the design of reduced order compensators for stochastic systems. Special emphasis is placed on optimization using a quadratic performance criterion. Both continuous and discrete time linear dynamical systems are considered, and state space system representation is used throughout the book. It provides a coherent view of the recent theory of reduced order theory and its applications including a wide range of application problems, solutions and unresolved issues.