The 27 papers in this volume survey various aspects of the theory of order. These have been grouped into nine sections illustrating some of the main mathematical themes and applications in the theory. These papers were written for the “Conference on ordered sets and their applications” (I’ARBRESLE, july 1982). This international meeting, the fourth devoted to the theory of order (following BANFF, 1981; MONTEREY , 1959, CHARLOTTESVILLE, 1938) - will shortly be succeeded by two others (BANFF and LUMINY, 1984). This continuing activity, and other signs such as the appearance of the new journal ORDER, suggests that there is an increasing recognition of the importance of order and an acceleration in the development of its theory. All this calls for some interpretation of the role of order in the general landscape of mathematics. Editing the present work has also led us to consider this question, and we offer here some of our thoughts on this matter to the reader.