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§This volume contains the papers presented at the Oxford University Computing Laboratory Programming Research Group 4th Annual Z User Meeting, held on 15 December 1989 at the University of Oxford, UK. This meeting provided an opportunity for Z Users to meet and to hear about the latest developments in both the theoretical and practical aspects of Z. The papers cover recent research on the formal notation of Z, with descriptions of its application in industry. Z tools and support environments are also described. The mathematical concepts and notational conventions we know of as Z were first proposed around 1981. Its origins were in line with the objectives of the PRG - to establish a mathematical basis for program ming concepts and to verify the work by case studies with industry. Hence among early Z users some were from academic circles, with interests in the mathematical basis of programming; others came from industry and were involved with pilot projects and case studies linked with the Programming Research Group. Four years ago we had the first Z User Meeting, a fairly modest affair with representatives more or less equally divided between academia and industry. At the first meeting there were, as in this meeting, a variety of technical papers, reports of work in progress and discussions. A number of people from industry came along, either because they had begun to use Z or were curious about the new direction. In the discussion sessions at the end of the meeting, there were calls from attendees for the establishment of a more stable base for the notation, including work on its documentation and standards. Many of these requests have now been satisfied and the notation is now being proposed for standards development.