This is the fourth international conference on quasicrystals and the first to be held in the United States. Topics to be discussed include understanding the geometry and chemical decorations of the quasicrystal structures, detailed structural studies on large, single quasicrystals, and the formation, stability, and physical properties of quasicrystals. New frontiers in quasicrystal research are covered, including diffraction and dynamics of synthetic non-periodic structures. %%% While similar to crystals in many respects, quasicrystals have important differences that may lead to novel behavior. Some models suggest exotic electronic properties. Unusual magnetic behavior may result from the extremely high symmetry about certain atomic sites.