This book is based mostly on the reports presented at the XVth International lahn-Teller Symposium on Vibronic Interactions in Crystals and Molecules and NATO Advanced Research Workshop Colossal Magnetoresistance and Vibronic Interactions that took place at Boston on August 16-22 of the year 2000. This is the first time the Symposium took place in the USA where recently the giant splash of the attention to the 1 ahn-Teller effect occurred. This tremendous interest to the field all over the world is reflected not only in the numerous publications in many American and European 10urnals, but of the leading scientists from additionally in the Symposium’s participation the well known Universities, National Laboratories and industrial companies, which was the largest in the history of the Symposium. The renaissance of the 1ahn-Teller physics is closely related to the three fundamental discoveries in science. The most significant among them is the discovery of high-Tc superconductivity by K. -A. Muller and G. Bednorz, for whom the 1ahn-Teller idea was the motivation in their search. The result of this search is well known - a wide spectrum of the 1ahn-Teller ion based materials with Tc between 24K and 135K were found. The second discovery is the existence of a new polymorph of carbon - the C60. The microscopic analysis of all physical, chemical and biological properties of the buckyballs is based on 1ahn-Teller type of interactions. The third is colossal magnetoresistance.