Within the course System Theory for Control, we deepen and broaden the knowledge of linear systems for the purpose of formulating and solving control problems. Moreover, students achieve to acquire in-depth insight in linear control theory that forms the basics for many other control courses and deepen the insight in the relations between models of internal behaviour (state-space models) and models that describe input/output behavior (impulse response, transfer functions/matrices). All of this includes basic realization theory and controllability, observability, and Jordan canonical forms. Stability and basic Lyapunov theory (quadratic Lyapunov functions) will be introduced. The students will acquire knowledge on the possibilities and limitations of the system behaviour, based on fundamental properties of state-space models: Controllability and stabilisability, and their relation with the stabilisation problem using state feedback on the one hand, and observability and detectability, and their relation with the state reconstruction problem based on measured outputs (i.e. observer design) on the other hand. Classical Linear Quadratic Control methods (LQR) and Kalman filtering will be discussed as well.