In 1854 B Riemann introduced the notion of curvature for spaces with a familyof inner products. There was no significant progress in the general case until1918 ... » 

In 1854 B Riemann introduced the notion of curvature for spaces with a familyof inner products. There was no significant progress in the general case until1918 when P Finsler studied the variation problem in regular metric spaces.Around 1926 L Berwald extended Riemanns notion of curvature to regular metricspaces and introduced a new quantity Berwald curvature. Since then Finslergeometry has developed steadily. In his Paris address in 1900 D Hilbertformulated 23 problems the 4th and 23rd problems being in Finslers category.Finsler geometry has broader applications in many areas of science and willcontinue to develop through the efforts of many geometers around the world.Usually the methods employed in Finsler geometry involve very complicatedtensor computations. Sometimes this discourages beginners. Viewing Finslerspaces as regular metric spaces The Author discusses the problems from themodern metric geometry point of view. The book begins with the basics onFinsler spaces including the notions of geodesics and curvatures then dealswith basic comparison theorems on metrics and measures and their applicationsto the Levy concentration theory of regular metric measure spaces and GromovsHausdorff convergence theory. «