Observations of distant supernovae have recently provided startling evidence of the accelerating expansion of the Universe. The reliability of this finding and its profound implications for both the study of supernovae and cosmology are the subject of this exciting volume. Here, articles by leading experts explore the theory of Type Ia supernovae, observational astronomy, and cosmology. In addition, they examine observational data, the nature of the likely progenitor binary systems, the outburst mechanisms of Type Ia supernovae events, and cosmological implications. This is a unique and wide-ranging review of one of the most dramatic and controversial results in contemporary astronomy.