The chapter provides the relevant language and techniques needed for the use of linear, continuous, and discrete-time state-space models in later chapters. It includes both time and frequency domain modelling tools, the elements of linear quadratic optimal tracking control relevant to Iterative Learning Control, and an introduction to operator methodologies for systems analysis. The reader may find it useful to peruse the last Sect. 2.15 as the notation defined precisely there is used from time to time in the preceding sections.