This volume represents the refereed proceedings of the Third International Conference on Finite Fields and Applications held at the University of Glasgow, Scotland, 11–14 July, 1995, where it was hosted by the Department of Mathematics. The conference, often referred to as Fq3, was the successor of two other international conferences concerning finite fields held at the University of Nevada, Las Vegas, USA, in August 1991 and in August 1993. The Organising Committee comprised Steve Cohen, Stuart Hoggar, Bob Odoni (all of the University of Glasgow), James Hirschfeld (University of Sussex), Gary Mullen (Pennsylvania State University), Harald Niederreiter (Austrian Academy of Sciences) and Peter Shiue (University of Nevada, Las Vegas).

Finite fields with their tight structure are intrinsically fascinating; further, their study is now recognised to be extremely useful in diverse areas of pure and applicable mathematics, including aspects of number theory, algebra, analysis and algebraic geometry and, at the same time, manifold aspects of information theory, computer science and engineering. For example, coding theory is enriched by deep ideas, crucially involving finite fields, on exponential sums, function fields and linear algebra, and in turn, has stimulated further questions for finite field research. Indeed, what is particularly exciting in current activity is the interplay between various areas, within pure mathematics itself and within those having definite applications. A further sign of this vitality is the emergence in 1995 of the journal Finite Fields and Their Applications published by Academic Press.