Mathematical Preliminaries -- Stabilizing Switching for Autonomous Systems -- Controllability, Observability, and Normal Forms -- Feedback Stabilization -- Optimization -- Conclusions and Perspectives.Switched linear systems have a long history in the control literature but-along with hybrid systems more generally-they have enjoyed a particular growth in interest since the 1990s. The large amount of data and ideas thus generated have, until now, lacked a co-ordinating framework to focus them effectively on some of the fundamental issues such as the problems of robust stabilizing switching design, feedback stabilization and optimal switching. This deficiency is resolved by Switched Linear Systems which features: • nucleus of constructive design approaches based on canonical decomposition and forming a sound basis for the systematic treatment of secondary results; • theoretical exploration and logical association of several independent but pivotal concerns in control design as they pertain to switched linear systems: controllability and observability, feedback stabilization, optimization and periodic switching; • a reliable foundation for further theoretical research as well as design guidance for real life engineering applications through the integration of novel ideas, fresh insights and rigorous results. Primarily intended for researchers and engineers in the systems and control community, postgraduate students will also discover that this is perfect complementary reading especially for those studying intelligent, adaptive or robust control.