This is a project to hold a five-day Research Symposium on Fermat's Last Theorem. Recent results on this famous unsolved conjecture argue that this is a felicitous time for such a Symposium. The Symposium will be built around ten lectures -- two each day -- by Professor John Tate of Harvard University. In addition, there will be sessions organized by Professor John Selfridge of Northern Illinois University on numerical approaches to the conjecture. Finally, there will be sessions for contributed papers, research ideas, and discussion. The wealth of mathematics that has been engendered by attempts to settle Fermat's Last Theorem is staggering, and recent results have led to generalizations and more conjectures related to the problem. These provide fertile grounds for more research ideas, and they will be explored in the course of the Tate lectures and the attendant Symposium activities. The sessions will be videotaped.