Until 1985, the chemical element Carbon was only known to exist in two forms -- diamond and graphite. This changed when Kroto and co-workers discovered an entirely new form of carbon, which became known as C60 or the fullerene molecule. (This discovery later led to their award of the 1996 Nobel Prize in Chemistry.) The original discovery of C60 was in the soot produced from the laser ablation of graphite. Since then, other methods of production have been developed. It is also thought that isolated C60 molecules may be found in stars and interstellar media. It was soon discovered that C60 is not the only ball-like carbon molecule possible (although it is the most stable and the most dominant). The rugby-ball shaped C70 molecule is another possibility. In nanotechnology, the potential applications of carbon nanotubes (formed by combining hexagonal rings of carbon atoms only, rather than hexagons and pentagons as in C60) for very small electronic devices are currently the subject of much activity. This book presents research advances from around the globe.