Kalman filters are based on the description of a physical dynamic system in state space and thus leverage these advantages. For this reason, the following chapter addresses the description of such systems in state space. It explains how differential equations can be transformed into state-space representations and how the two system properties, “observability” and “controllability,” are defined. Since Kalman filters are used in computers where only discrete-time values are available, the chapter concludes, following the solution of the state equation, with a discussion of the description of discrete-time systems, which is particularly important for Kalman filters.