State-space methods form the basis of modern control theory. This textbook is devoted to a description of these methods in the analysis of linear multiple-input, multiple-output dynamics systems. Throughout, continuous-time and discrete-time systems are treated in parallel, as are time-varying and classical time-invariant systems, thereby highlighting their similarities and differences. Following a chapter, which sets out the basic concepts and definitions, state equations of finite dimensional systems and their solutions, are discussed in detail. The principles of time-domain and frequency-domain analysis are then presented, as are the properties and applications of the Z-transformation. One chapter deals with the controllability and observability of linear systems and a separate chapter discusses stability. A useful tutorial review of the key results from matrix theory and linear algebra is given in the Appendix. In addition to illustrative examples, which are worked out in detail, numerous problems are available at the end of each chapter. The book will be of great value to graduate students of aeronautical, electrical, and mechanical engineering, or anyone who wants to acquire a solid background in the fundamentals of linear systems and modern control systems.