Introducing readers to adaptive systems in a rigorous but elementary fashion, this text emphasizes the mainstream developments in adaptive control and signal processing of linear discrete time systems. A unified framework is developed whereby the reader can analyze and understand any adaptive system in the literature. The so-called equilibrium analysis facilitates an understanding of the limitations and potential of adaptive systems in a transparent fashion; while the behavioural approach to linear systems plays an essential role at some key points in the text. So-called universal controllers are presented in some detail. Each chapter is accompanied by exercises that aim to develop certain aspects of the theory, as well as to give the reader a better understanding of the actual behaviour of adaptive systems.