Z is a set of conventions for presenting mathematical text, chosen to make it convenient to use simple mathematics to describe computing systems. I say computing systems because Z has been used to model hardware as well as software.

Z is a mature notation. Conceived in the late 1970s, it developed through the 1980s in collaborative projects between Oxford University and industrial partners, including IBM and Inmos (a semiconductor producer). The first Z reference manual to be widely published benefited from this long experience when it finally appeared in 1989. At this writing a draft Z standard (including a formal semantics) is being considered by the American National Standards Institute (ANSI), the British Standards Institute (BSI) and the International Organization for Standardization (ISO). Z has served as the basis for other notations, including several variants adapted for object-oriented programming.

Z is a model-based notation. In Z you usually model a system by representing its state — a collection of state variables and their values — and some operations that can change its state. A model that is characterized by the operations it describes is called an abstract data type (ADT). This modelling style is a good match to imperative, procedural programming languages that provide a rich collection of data types, and also to some physical systems (such as digital electronics) that include storage elements. Z is also a natural fit to object-oriented programming.