Inverse problems are concerned with determining causes for observed or desired effects. Problems of this type appear in many application fields both in science and in engineering. The mathematical modelling of inverse problems usually leads to ill-posed problems, i.e., problems where solutions need not exist, need not be unique or may depend discontinuously on the data. For this reason, numerical methods for solving inverse problems are especially difficult, special methods have to be developed which are known under the term "regularization methods." This volume contains twelve survey papers about solution methods for inverse and ill-posed problems and about their application to specific types of inverse problems, e.g., in scattering theory, in tomography and medical applications, in geophysics and in image processing. The papers have been written by leading experts in the field and provide an up-to-date account of solution methods for inverse problems.

This volume contains thirteen papers and one extended abstract based on talks given at the symposium "Inverse Problems and Optimal Design in Industry" which took place from July 8 to 10, 1993, in Philadelphia. This symposium was jointly organized by ECMI an SIAM, with the cooperation of IMA (Minnesota), INRIA, and SIMA . The organizing committee was co-chaired by the editors of this volume and included, in addition, V. Boffi (SIMAI, Italy) G. Chavent (INRIA, France), D. Colton (University of Delaware, USA) and A. Friedman (IMA, USA). Financial support from the U. S. Department of Energy is gratefully acknowledged. The primary aim of this meeting, which is reflected in this volume, was to bring to gether mathematicians working in industry. who treat inverse and optimal design problems in their practical work and mathematiCians from academia who are active in mathem atical research in these fields in order to strenghten the contacts between industry and academia. Thus, this volume contains (refereed) papers both on inverse and optimal design problems as they appear in European, American and Japanese industry, and on analytical and numerical techniques for solving such types of problems. The topics treated include multi-disciplinary design optimization in aerospace industry, inverse problems in steel industry, inverse and optimum design problems in optics and photographic science, inverse electromagnetic problems including impedance imaging, and inverse problems in the petroleum industry. There were two styles of presentation of topics. One was discussion sessions."