This volume is based to a large extent on the Linear Logic Workshop held June 14–18, 1993 at the MSI and partially supported by the US Army Research Office and the US Office of Naval Research. The workshop was attended by about 70 participants from the USA, Canada, Europe, and Japan. The workshop program committee was chaired by A. Scedrov (University of Pennsylvania) and included S. Abramsky (Imperial College, London), J.-Y. Girard (CNRS, Marseille), D. Miller (University of Pennsylvania), and J. Mitchell (Stanford). The principal speakers at the workshop were J.-M. Andreoli, A. Blass, V. Danos, J.-Y. Girard, A. Joyal, Y. Lafont, J. Lambek, P. Lincoln, M. Moortgat, R. Pareschi, and V. Pratt. There were also a number of invited 30 minute talks and several software demonstration sessions.

Our intention was not only to publish a volume of proceedings. We also wanted to give an overview of a topic that started almost 10 years ago and that is of interest for mathematicians as well as for computer scientists. For these reasons, the book is divided into 5 parts:

1. Categories and Semantics

2. Complexity and Expressivity

3. Proof Theory

4. Proof Nets

5. Geometry of Interaction

The five parts are preceded by a general introduction to Linear Logic by J.-Y. Girard. Furthermore, parts 2 and 4 start with survey papers by P. Lincoln and Y. Lafont. We hope this book can be useful for those who work in this area as well as for those who want to learn about it. All papers have been refereed and the editors are grateful to A. Scedrov who took care of the refereeing process for the papers written by the the editors themselves.