Observability and Controllability for Finite-dimensional Systems -- Operator Semigroups -- Semigroups of Contractions -- Control and Observation Operators -- Testing Admissibility -- Observability -- Observation for the Wave Equation -- Non-harmonic Fourier Series and Exact Observability -- Observability for Parabolic Equations -- Boundary Control Systems -- Controllability -- Appendix I: Some Background on Functional Analysis -- Appendix II: Some Background on Sobolev Spaces -- Appendix III: Some Background on Differential Calculus -- Appendix IV: Unique Continuation for Elliptic Operators.