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Hybrid dynamical systems are a class of complex systems that involve interacting discrete-event and continuous-variable dynamics. They are important in applications in embedded systems, cyber-physical systems, robotics, manufacturing systems, traffic management, bio-molecular networks, and have recently been at the centre of intense research activity in the control theory, computer-aided verification, and artificial intelligence communities. Theory of Hybrid Dynamical Systems provides a tutorial introduction to this multidisciplinary research area. A number of fundamental topics, such as modelling, abstraction, verification, supervisory control, stability analysis, stabilization, and optimal control of hybrid systems are introduced and discussed. Additionally, more advanced topics are briefly discussed and references are given for further study.