This is a proposal for a CMBS sponsored research conference on division algebras. The week long conference will be held at Colorado State University in Fort Collins Colorado in the summer of 1998. The principal speaker, David Saltman, is an authority on the subject. He is both one of the main contributors to recent advances in the subject and a popularizer of the area through his students, collaborators and lectures. The subject itself is concrete and can be approached in an elementary way. Division algebras are currently an exciting area of research, with both knowledge of these objects and the application of this knowledge expanding rapidly. This makes the proposed subject an ideal one for a research conference appealing to a broad audience. For more information contact Frank DeMeyer, Department of Mathematics, Colorado State University (e-mail demeyer@math.colostate.edu) ______________________