An Introduction to Riemann-Finsler Geometry (Graduate Texts in Mathematics, 200)

The authors claim to turn the subject of Finsler geometry with this bookinto a more teachable one and to have a candid style of writing.This is definitly true for the first 50 pages, where the concepts ofFinsler geometry are very well explained and the exercisesare manageable and perfectly interrelated with the text.Then the Chern connection and the curvature tensor of Finsler geometrydrop out of the heaven without any explanation of the ideas leading to theseconstructions. So one has to derive them alone. In doing so oldertexts on Finsler geometry like the Grundlehren text of Rund are morehelpful than this volume.But the book was apparently prepared with great care. The layout must be calledbeautyful and it really facilitates reading this book. Many referencesto the literature and classical papers of the subject are included. So beginners,which want to get a first aquaintance in Finsler geometry, find at least some help.