The serendipitous discovery of the fullerenes by Kroto, Curl and Smalley in 1985, and the isolation and characterization of C60 by Kratschmer and Huffman in 1990 has caused an epidemic of research in this field. As a result, basic research on fullerenes has generated new knowledge as published in thousands of journal papers. The nuclear and radiation approaches, however, have been somewhat neglected in books dedicated to fullerene sciences, although these approaches have generated very interesting knowledge on the structure and composition of these new all-carbon molecules. This monograph intends to bridge this gap by dealing with the various aspects of nuclear sciences as applied to the generation of new knowledge in fullerene sciences. Ten chapters appear in this volume and were chosen to present a panoramic view and to provide theoretical perspectives, research methods, and experimental results on the topic. This book should serve both as an introduction to the subfield and as an aid to setting an agenda for scientists interested in this area of research. This is the first volume in a series devoted to the developments in fullerene science.