The Jahn-Teller effect is manifested in a variety of phenomena in physics, chemistry and biochemistry, in many types of crystals and molecules. This book deals with fundamental questions of the quantum mechanics of systems with orbital electrons, concentrating on novel phenomena and materials such as colossal magnetoresistance, high Tc superconductivity, buckminsterfullerenes, magnetic materials and biologically important clusters. All chapters share a common general approach to the problems, based on the analysis of vibronic interaction: electron-vibrational interaction in molecules and electron-phonon interaction in crystals.