The ICMS Instructional Conference between 30 March and 9 April 1998 was one of a series of highly successful such conferences held under the auspices of the International Centre of Mathematical Sciences in Edinburgh, Scotland. Some of these meetings have been held in the house where Maxwell was born, which is now the ICMS administrative headquarters. The lectures for larger meetings, such as this one, were in the James Clerk Maxwell Building of the University of Edinburgh in a different part of the city. Accommodation for the meeting was provided for all speakers and audience in the Pollock Halls of Residence belonging to the University and providing a refreshing twenty minute walk to and from the lectures.

The subject of this meeting was Spectral Theory and Geometry, and the format followed that of earlier meetings. Twelve principal speakers were invited to give lecture courses of three hours each, graded into three levels, Introductory, Medium and Advanced (see the list below). There were several exchanges before the meeting about the contents of the introductory lectures, since these had to provide the core material for all of the later courses. These were all given by world experts, who provided organised surveys of their fields, with proofs in many cases. This volume contains articles by most of the lecturers. Many of these go beyond what they could present within the time limits of the conference, and we are most grateful to them for undertaking the considerable amount of work involved in producing the lecture notes.