PRELIMINARY TEXT. DO NOT USE. Finsler geometry is a metric
generalization of Riemannian geometry and has become a comparatively
young branch of differential geometry. Although Finsler geometry has its
genesis in Riemann's 1854 "Habilitationsvortrag," its systematic study
was not initiated until 1918 by Finsler, and the fundamentals were not
completely formulated until the mid-thirties. Later, however, the field
underwent a rapid development by mathematicians and physicists of many
countries. The main purpose of this book is to study the metric geometry
of Finsler manifolds. Portions of the book generalize some standard
concepts from Riemannian geometry to the Finsler setting, while other