'We hope that this small volume will suggest directions of synergy and contact for future researchers to build upon, creating connections and making discoveries that will help explain some of the many mysteries of computation' - from the Preface. Finite model theory can be succinctly described as the study of logics on finite structures. It is an area of research existing between mathematical logic and computer science. This area has been developing through continuous interaction with computational complexity, database theory, and combinatorics. The volume presents articles by leading researchers who delivered talks at the 'Workshop on Finite Models and Descriptive Complexity' at Princeton in January 1996 during a DIMACS-sponsored Special Year on Logic and Algorithms. Each article is self-contained and provides a valuable introduction to the featured research areas connected with finite model theory.