This new edition of Introduction to Lattices and Order is substantially different from the original one published in 1990. We believe that the revision greatly enhances the book's usefulness and topicality. Our overall aims however remain the same: to provide a textbook introduction which shows the importance of the concept of order in algebra, logic, computer science and other fields and which makes the basic theory accessible to undergraduate and beginning graduate students in mathematics and to professionals in adjacent areas.

In preparing the new edition we have drawn extensively on our teaching experience over the past 10 years and on helpful comments from colleagues. We have taken account of important developments in areas of application, in particular in computer science. Almost all the original material is included, but it has been completely re-organized. Some new material has been added, most notably on Galois connections and fixpoint calculus, and there are many new exercises.

Our objectives in re-arranging the material have been:

• to present elementary and motivational topics as early as possible, for pedagogical reasons;

• to arrange the chapters so that the first part of the book contains core material, suitable for a short, first course;

• to make it easy for particular interest groups to pick out just the sections they want.