This is a collection of ten refereed papers presented at an international Summer School and Conference on Proof Theory held at Bodington Hall, Leeds University between 24th July and 2nd August 1990. The meeting was held under the auspices of the “Logic for Information Technology” (Logfit) initiative of the UK Science and Engineering Research Council, in collaboration with the Leeds Centre for Theoretical Computer Science (CTCS). The principal funding came from SERC Logfit under contract SO/72/90 with additional contributions gratefully received from the British Logic Colloquium and the London Mathematical Society. There were 100 participants representing at least twelve different countries: Belgium, Canada, Estonia, France, Germany, Italy, Japan, Norway, Sweden, Switzerland, USA and UK.

The first three papers printed here represent short lecture courses given in the summer school and are intended to be of a more instructional nature, leading from basic to more advanced levels of ‘pure’ proof theory. The others are conference research papers reflecting a somewhat wider range of topics, and we see no better way of ordering them than alphabetically by author.

The programme of lectures given at the meeting is set out overleaf. Though not all of the invited speakers were able to contribute to this volume we believe that what remains provides rich flavours of a tasty subject.