The three subjects of this book all began life in the provinces of applicable mathematics. Design theory originated in statistics (its name reflects its initial use, in experimental design); codes in information transmission; and graphs in the modelling of networks of a very general kind (in the first instance, the bridges of Königsberg). All three have since become part of mainstream discrete mathematics.

We have not tried to write a textbook on three individual topics. Instead, our goal is more limited: we want to explore some of the ways in which the three topics have interacted with each other, with results and methods from one area being applied in another. Indeed, we believe that discrete mathematics is better defined by its methods than by its subject-matter, and our approach reflects this.

The book has its origins in the notes of two series of lectures given by the authors at Westfield College, London, at the invitation of Dan Hughes. The audience at those lectures consisted of design theorists, and our job was to show them that graphs and codes could be useful to them. The notes subsequently appeared in the London Mathematical Society Lecture Note Series in 1975, and in a considerably revised form in 1980. We tried then to make the notes accessible to a wider audience by adding an introductory chapter on design theory.

In the intervening decade, we have become aware that a number of students used the book as a textbook. Their task was not made easier by the ‘research notes’ style in which many assertions are left without proof.