  The geometry and analysis on Finsler manifolds is a very important part of
Finsler geometry. In this article, we introduce some important and fundamental
topics in global Finsler geometry and discuss the related properties and the
relationships in them. In particular, we optimize and improve the various
definitions of Lie derivatives on Finsler manifolds. We also characterize the
gradient vector fields and obtain a gradient estimate for any smooth function
on a Randers manifold.
