Because of the high symmetry involved, the Jahn-Teller effect is the natural starting point for considering electron-phonon (or ) interactions in icosahedral molecules. This work is the first comprehensive theoretical analysis of the Jahn-Teller interaction in C60 and other icosahedral complexes. The importance of this research derives in part from the increasing, widespread interest in C60 and other molecular 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. In particular, a chapter is devoted to the connection between the theory and experimental observations, such as ESR (electron spin resonance) effects and molecular spectra. Earlier books have discussed the theory of Jahn-Teller interactions in lower symmetry structures (cubic, tetrahedral, tetragonal, trigonal,...); this is the first that focuses on the new icosahedral systems, whose most famous example is Buckminsterfullerene, C60. The book's authors have over fifty years of combined research experience into the theoretical aspects of the Jahn-Teller effect.