This volume consists ofsurvey articles on current topics in computational wave prop­ agation and inverse problems, written by leading experts in their respective fields. The idea to compile such a volume arose in conjunction with the LMS Durham Symposium on Computational Methods for Wave Propagation in Direct Scattering held at the University of Durham from 15th-25th July 2002, which we jointly or­ ganised. The meeting, attended by 70 participants from the UK and overseas, was structured around a number of short, three lecture, survey courses on a range of top­ ics on computational wave propagation and inverse problems beginning at the level of a graduate student. We were delighted to secure the participation of distinguished international researchers to present these lectures. We felt that it would be valuable to record this material for the benefit of a wider audience, and the idea was hatched that the individual lecturers should be invited to contribute a survey article. Fortunately, many of the speakers not only agreed to undertake this arduous task, but produced what we hope you will agree are the high quality contributions found in this volume. Finally, it is a pleasure to thank the Engineering and Physical Sciences Research Council of Great Britain and the London Mathematical Society for providing the generous support that allowed the meeting to take place. Mark Ainsworth Glasgow, 2003 Penny Davies Dugald Duncan Paul Martin Bryan Rynne Contents New Results on Absorbing Layers and Radiation Boundary Conditions Thomas Hagstrom .