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On March 17-19 and May 19-21,1995, analysis seminars were organized jointly at the universities of Copenhagen and Lund, under the heading "Danish-Swedish Analysis Seminar". The main topic was partial differen- tial equations and related problems of mathematical physics. The lectures given are presented in this volume, some as short abstracts and some as quite complete expositions or survey papers. They span over a large vari- ety of topics. The most frequently occurring theme is the use of microlocal analysis which is now important also in the study of non-linear differential equations although it originated entirely within the linear theory. Perhaps it is less surprising that microlocal analysis has proved to be useful in the study of mathematical problems of classical quantum mechanics, for it re- ceived a substantial input of ideas from that field. The scientific committee for the invitation of speakers consisted of Gerd Grubb in Copenhagen, Lars Hormander and Anders MeHn in Lund, and Jo- hannes Sjostrand in Paris. Lars Hormander and Anders Melin have edited the proceedings. They were hosts of the seminar days in Lund while Gerd Grubb was the host in Copenhagen. Financial support was obtained from the mathematics departments in Copenhagen and Lund, CNRS in France, the Danish and Swedish Na- tional Research Councils, Gustaf Sigurd Magnuson's foundation at the Royal Swedish Academy of Sciences, and the Wenner-Gren foundation in Stockholm. We want to thank all these organisations for their support.