Originally published in 1969, this classic textbook provides a solid foundation for learning about dynamical systems, and encourages students to develop a reliable intuition for problem solving. The theory of linear systems has been the bedrock of control theory for fifty years and has served as the springboard for many significant developments, all the while remaining impervious to change. Since linearity lies at the heart of much applied mathematical analysis, a firm grounding in its central ideas is essential. This book touches upon many standard topics in applied mathematics, develops the theory of linear systems in a systematic way, making as much use as possible of vector ideas, and contains a number of examples and many exercises. The book is recommended for first-year graduate students. The topics covered form the core of fields such as optimal control, estimation, stability, electrical networks, and control of distributed systems.