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.

Part I. Mathematics of Distances.- 1 General Definitions.- 2 Topological Spaces.- 3 Generalization of Metric Spaces.- 4 Metric Transforms.- 5 Metrics on Normed Structures.- Part II. Geometry and Distances.- 6 Distances in Geometry.- 7 Riemannian and Hermitian Metrics.- 8 Distances on Surfaces and Knots.- 9 Distances on Convex Bodies, Cones and Simplicial Complexes.- Part III. Distances in Classical Mathematics.- 10 Distances in Algebra.- 11 Distances on Strings and Permutations.- 12 Distances on Numbers, Polynominals and Matrices.- 13 Distances in Functional Analysis.- 14 Distances in Probability Theory.- Part IV. Distances in Applied Mathematics.- 15 Distances in Graph theory.- 16 Distances in Coding Theory.- 17 Distances and Similarities in Data Analysis.- 18 Distances in Systems and Mathematical Engineering.- Part V. Computer-Related Distances.- 19 Distances on Real and Digital Planes.- 20 Voronoi Diagram Distances.- 21 Image and Audio Distances.- 22 Distances in Networks.- Part VI. Distances in Natural Sciences.- 23 Distances in Biology.- 24 Distances in Physics and Chemistry.- 25 Distances in Earth Science and Astronomy.- 26 Distances in Cosmology and Theory of Relativity.- Part VII. Real-World Distances.- 27 Length Measures and Scales.- 28 Distances in Applied Social Sciences.- 29 Other Distances

Part I. Mathematics of Distances.- 1 General Definitions.- 2 Topological Spaces.- 3 Generalization of Metric Spaces.- 4 Metric Transforms.- 5 Metrics on Normed Structures.- Part II. Geometry and Distances.- 6 Distances in Geometry.- 7 Riemannian and Hermitian Metrics.- 8 Distances on Surfaces and Knots.- 9 Distances on Convex Bodies, Cones and Simplicial Complexes.- Part III. Distances in Classical Mathematics.- 10 Distances in Algebra.- 11 Distances on Strings and Permutations.- 12 Distances on Numbers, Polynominals and Matrices.- 13 Distances in Functional Analysis.- 14 Distances in Probability Theory.- Part IV. Distances in Applied Mathematics.- 15 Distances in Graph theory.- 16 Distances in Coding Theory.- 17 Distances and Similarities in Data Analysis.- 18 Distances in Mathematical Engineering.- Part V. Computer-Related Distances.- 19 Distances on Real and Digital Planes.- 20 Voronoi Diagram Distances.- 21 Image and Audio Distances.- 22 Distances in Internet and Similar Networks.- Part VI. Distances in Natural Sciences.- 23 Distances in Biology.- 24 Distances in Physics and Chemistry.- 25 Distances in Geography, Geophysics and Astronomy.- 26 Distances in Cosmology and Theory of Relativity.- Part VII. Real-World Distances.- 27 Length Measures and Scales.- 28 Distances in Applied Social Sciences.- 29 Other Distances.