The Theory of Linear Systems presents the state-phase analysis of linear systems. This book deals with the transform theory of linear systems, which had most of its success when applied to time-invariant systems. Organized into nine chapters, this book begins with an overview of the development of some properties of simple differential systems that are mostly of a nonalgebraic nature. This text then presents a brief treatment of vector spaces, matrices, transformations, norms, and inner products. Other chapters deal with the inductive process used to define dynamical systems. This book discusses as well the existence and uniqueness theorem for the solutions of a homogeneous linear differential system. The final chapter deals with the abstract concept of a dynamical system and derives properties of these systems. This book is a valuable resource for advanced graduate students in areas such as economics and bioengineering. Engineers engaged in systems design will also find this book useful.