This updated and revised second edition of the leading reference volume on distance metrics includes a wealth of new material that reflects advances in a developing field now regarded as an essential tool in many areas of pure and applied mathematics.   Its publication coincides with intensifying research efforts into metric spaces and especially distance design for applications. Accurate metrics have become a crucial goal in computational biology, image analysis, speech recognition and information retrieval.   The content focuses on providing academics with an invaluable comprehensive listing of the main available distances. As well as standalone introductions and definitions, the encyclopedia facilitates swift cross-referencing with easily navigable bold-faced textual links to core entries, and includes a wealth of fascinating curiosities that enable non-specialists to deploy research tools previously viewed as arcane. Its value-added context is certain to open novel avenues of research.