Singularity theory encompasses many different aspects of geometry and topology, and an overview of these is represented here by papers given at the International Singularity Conference held in 1991 at Lille. The conference attracted researchers from a wide variety of subject areas, including differential and algebraic geometry, topology, and mathematical physics. Some of the best known figures in their fields participated, and their papers have been collected here. Contributors to this volume include G. Barthel, J.W. Bruce, F. Delgado, M. Ferrarotti, G.M. Greuel, J.P. Henry, L. Kaup, B. Lichtin, B. Malgrange, D. Mond, L. Narváez, V. Neto, A.A. Du Plessis, R. Thom and M. Vaquié.