Formal design methods are becoming increasingly recognised as being useful for specifying complex systems. Incorporating formal methods in the early stages of a design process introduces the possibility of using mathematical techniques, hence improving the effectiveness of a design process. The Z notation has been applied mainly to specifying software, although it has also been used for specifying hardware and general systems. The Z notation fulfils two functions in this thesis. The first function is as a notation for representing specifications of complex systems, and the second function is as a notation for representing implementations of the same complex systems. The suitability of the Z notation for these functions is investigated in three studies. Both the specifications and implementations are represented as unified collections of Schemas that describe the behaviour in response to each set of input conditions. In each of the studies, both the specifications and implementations of the complex system take place at an early stage in a design process. Throughout this thesis non rigorous proof sketches prove that the implementations meet the requirements of the specifications.