Computer science aims to explain the way computational systems behave for us. The notion of calculational process, or algorithm, is a lot older than computing technology; so, oddly enough, a lot of computer science existed before modern computers. But the invention of real stored-program computers presented enormous challenges; these tools can do a lot for us if we describe properly what we want done. So computer science has made immense strides in ways of presenting data and algorithms, in ways of manipulating these presentations themselves as data, in matching algorithm description to task description, and so on. Technology has been the catalyst in the growth of modern computer science.

The first large phase of this growth was in free-standing computer systems. Such a system might have been a single computer program, or a multi-computer serving a community by executing several single programs successively or simultaneously. Computing theorists have built many mathematical models of these systems, in relation to their purposes. One very basic such model - the λ-calculus - is remarkably useful in this role, even if it was designed by Alonzo Church around 1940.

The second phase of the growth of computer science is in response to the advent of computer networks. No longer are systems freestanding; they interact, collaborate and interrupt each other. This has an enormous effect on the way we think about our systems. We can no longer get away with considering each system as sequential, goal-directed, deterministic or hierarchical; networks are none of these. So if we confine ourselves to such concepts then we remain dumb if asked to predict whether a network will behave in a proper - or an improper - way; for example, whether someone logging in to his bank may (as happened recently) find himself scanning someone else's account instead of his own.

The present book is a rigorous account of a basic calculus which aims to underpin our theories of interactive systems, in the same way that the λ-calculus did for freestanding computation. The authors are two of the original researchers on the π-calculus, which is now over ten years old and has served as a focus for much theoretical and practical experiment.