  In this paper we provide the complete classification of Kleinian groups of
Hausdorff dimensions less than $1.$ In particular, we prove that every purely
loxodromic Kleinian groups of Hausdorff dimension $<1$ is a classical Schottky
group. This upper bound is sharp. As an application, the result of \cite{H}
then implies that, every closed Riemann surface is uniformizable by a classical
Schottky group. The prove relie on the result of Hou \cite{Hou}, and space of
rectifiable $\G$-invariant closed curves.
