In Finsler geometry, we use calculus to study the geometry of regular inner
metric spaces. In this note I will briefly discuss various curvatures and their
geometric meanings from the metric geometry point of view, without going into
the forest of tensors.Comment: 17 pages, This article is for the 20th Winter School on Geometry and
Physics at Srni in Czech Republic. It was written during my visit at
Institute of Mathematics and Informatics (IMI) at University of Debrecen in
Hungary. The author would like to thank Dr. S. B\'{a}cs\'{o} and Dr. L. Kozma
for their great help and hospitalit
