The discovery of fullerenes, a new allotropic modification of carbon, is a prominent achievement of the late 20th century in chemistry. In this book, the authors present topical research in the study of the synthesis, properties and applications of fullerene. Topics discussed include phase equilibria in the fullerene-containing system; ionic compounds of fullerenes obtained by synthesis in solution; symmetrical features of fullerene structures in the fundamental domains theory of point symmetry groups; the biomedical application of fullerene; metal complex catalysts in the chemistry of fullerenes; functionalised nanofullerenes for hydrogen storage; self-assembly properties of fullerenes and the radiation induced phenomena in fullerenes.