This volume contains the proceedings of the summer school "Modern Methods of Optimization", held at the Schlof3 Thurnau of the University of Bayreuth, October 1-6, 1990. Like other branches of applied mathematics the area of optimization is undergoing a rapid development since the beginning of the computer age. Optimizaiton methods are of increasing importance for both, science and industry. The aim of the summer school was to present state-of-the-art knowledge by inviting 12 specialists from Op timization (and related fields) to present their areas of activity in the form of survey talks. This volume contains 10 of these presentations in slightly extended form. Most lectures started from an undergraduate level and outlinad the developments up to the latest scientifique achievements. This enabled the audience, consisting of about 45 students and young researchers, to get an excellent overview of the latest trends in Optimization as w~ll as a grasp of the breadth of its potential applications. Equally important to the success of the summer school was the "nonmeasurable" part of the activities inherent in such a summer school. Here the inspiring atmosphere of a place like Thurnau helped to establish numerous contacts between "teachers" and "students". The summer school was organized by the Universitii. t Bayreuth together with the Technische Hochschule Darmstadt and was generously sponsored by the Volkswagen stiftung and the Universitii. tsverein Bayreuth. Their interest in the meeting and their support is hereby gratefully acknowledged.