  Our aim in this paper is to classify the $3$-dimensional connected
differentiable global Bol loops, which have a non-solvable group as the group
topologically generated by their left translations and to describe their
relations to metric space geometries. The classification of global
differentiable Bol loops significantly differs from the classification of local
differentiable Bol loops. We treat the differentiable Bol loops as images of
global differentiable sections $\sigma :G/H \to G$ such that for all $r,s \in
\sigma (G/H)$ the element $rsr$ lies in $\sigma (G/H)$, where $H$ is the
stabilizer of the identity $e$ of $L$ in $G$.
