This paper is a revised version of the notes for the tutorial of D. Duval at ISSAC’98. We are indebted to the participants of the working group on sketches and computer algebra for their questions and suggestions, and to C.N.R.S. for its support. This document was processed with LATEX and XY-pic.

SKETCHES AND SPECIFICATIONS is a common denomination for several papers which deal with applications of Ehresmann’s sketch theory to computer science. These papers can be considered as the first steps towards a unified theory for software engineering. However, their aim is not to advocate a unification of computer languages; they are designed to build a frame for the study of notions which arise from several areas in computer science. These papers are arranged in two complementary families: REFERENCE MANUAL and USER’S GUIDE. The reference manual provides general definitions and results, with comprehensive proofs. On the other hand, the user’s guide places emphasis on motivations and gives a detailed description of several examples. These two families, though complementary, can be read independently. No prerequisite is assumed; however, it can prove helpful to be familiar either with specification techniques in computer science or with category theory in mathematics. These papers are under development, they are, or will be, available at: