The Oxford Topology Symposium was held in June 1989. Since techniques from topology and category theory have been used increasingly by theoretical computer scientists in recent years, it was decided to hold a special session at the symposium which would be devoted to the application of these topics in computer science. By holding this session in the context of the topology symposium, the organisers hoped to achieve a cross-fertilization between the communities they brought together - giving one a course of new problems with a more practical flavour, and the other a source of solutions and ideas. The session itself proved successful, attracting a large audience of mathematicians as well as computer scientists.The organizing committee decided to produce two separate proceedings for the conference. All those who had presented papers, plus a very few others, were invited to submit papers for these proceedings of the special session on topology and category theory in computer science.