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

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The authors claim to turn the subject of Finsler geometry with this book
into a more teachable one and to have a candid style of writing.
This is definitly true for the first 50 pages, where the concepts of
Finsler geometry are very well explained and the exercises
are manageable and perfectly interrelated with the text.

Then the Chern connection and the curvature tensor of Finsler geometry
drop out of the heaven without any explanation of the ideas leading to these
constructions. So one has to derive them alone. In doing so older
texts on Finsler geometry like the Grundlehren text of Rund are more
helpful than this volume.

But the book was apparently prepared with great care. The layout must be called
beautyful and it really facilitates reading this book. Many references
to 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.