Because of the high symmetry involved, the Jahn-Teller effect is the natural starting point for considering electron-phonon (or vibronic) interactions in icosahedral molecules. This work is the first comprehensive theoretical analysis of the Jahn-Teller interaction in C[subscript]60 and other icosahedral complexes. The importance of this research derives in part from the increasing, widespread interest in C[subscript]60 and other molecule clusters and their application in science and industry. The electrical and spectroscopic properties of fullerene and fulleride compounds depend intimately on the coupling between the electronic and vibrational modes of these systems, and this book addresses the fundamental theoretical questions. Earlier books have discussed the theory of Jahn-Teller interactions in lower symmetry structures (e.g. cubic, tetrahedral, tetragonal, and trigonal); this is the first that focuses on the new icosahedral systems, whose most famous example is Buckminster-fullerene, C[subscript]60.