Whilst improperly posed problems appear in several branches of applied and pure mathematics, this conference concentrated mainly on the practical treatment of ill- posedness. The participants came from 12 countries. The interchange of ideas reflected the spectrum of questions arising in connection with the subject of the conference, where currently progresses in research are made. This volume contains 17 papers presented at the con- ference. Focal points in the programme were: Problems of regularisation, parameter identification, free boundary and inverse problems in differential equations and inte- gral equations of the first kind. Problems, which appear in science, in technical fields and in medicine are dis- cussed as well as general operator equations. In a jOint discussion, several open problems have been worked out which are collected at the end of the volume. The editor's thanks go to all contributors and parti- cipants who made the conference a success; to the manage- ment of the institute with its unique atmosphere; to the Birkhauser Verlag for the possibility to publish the vo- lume in the well-known ISNM series; to Dr. P. Jochum (Mlin- chen) for assistance in organization and to Mrs. Chr. Rogg (Augsburg) for her excellent typing of several manuscripts.