From the 28th of February through the 3rd of March, 2001, the Department of Math- ematics of the University of Florida hosted a conference on the many aspects of the field of Ordered Algebraic Structures. Officially, the title was "Conference on Lattice- Ordered Groups and I-Rings," but its subject matter evolved beyond the limitations one might associate with such a label. This volume is officially the proceedings of that conference, although, likewise, it is more accurate to view it as a complement to that event. The conference was the fourth in wh at has turned into aseries of similar...