Mobile systems are everywhere. Palpable examples are mobile communication devices and the networks that span the Earth and reach out into Space. And less tangibly, there is mobile code and the wondrous weaving within the World Wide Web. An accepted science of mobile systems is not yet established, however. The development of this science is both necessary and challenging. It is likely that it will consist of theories offering explanations at many different levels. But there should be something basic that underlies the various theories.

This book presents the π-calculus, a theory of mobile systems. The π-calculus provides a conceptual framework for understanding mobility, and mathematical tools for expressing mobile systems and reasoning about their behaviours. We believe it is an important stepping-stone on the path to the science of mobile systems.

But what is mobility? When we talk about mobile systems, what are the entities that move, and in what space do they move? Our broad answer is based on distinguishing two kinds of mobility. In one kind, it is links that move in an abstract space of linked processes. For example: hypertext links can be created, can be passed around, and can disappear; the connections between cellular telephones and a network of base stations can change as the telephones are carried around; and references can be passed as arguments of method invocations in object-oriented systems. In the second kind of mobility, it is processes that move in an abstract space of linked processes. For instance: code can be sent over a network and put to work at its destination; mobile devices can acquire new functionality using, for instance, the Jini technology [AWO+99]; and procedures can be passed as arguments of method invocations in object-oriented systems.

The π-calculus treats the first kind of mobility: it directly expresses movement of links in a space of linked processes. There are two kinds of basic entity in the (untyped) π-calculus: names and processes. Names are names of links. Processes can interact by using names that they share. The crux is that the data that processes communicate in interactions are themselves names, and a name received in one interaction can be used to participate in another.