  We survey some basic geometric properties of the Funk metric of a convex set
in $\mathbb{R}^n$. In particular, we study its geodesics, its topology, its
metric balls, its convexity properties, its perpendicularity theory and its
isometries. The Hilbert metric is a symmetrization of the Funk metric, and we
show some properties of the Hilbert metric that follow directly from the
properties we prove for the Funk metric.
