Volumes on Finsler Spaces

The aim of this talk is to give an introduction to volumes on Finsler spaces. A Finsler metric on a manifold is defined as a Riemannian metric except that its restriction to a tangent plane is no longer an Euclidean norm but a Minkowski norm. Distinct definitions of volume should coincide in the Riemannian case. I will begin by explaining the notion of volume on a normed space in order to proceed to the Finsler case.