  In this paper we provide the complete classification of convex cocompact
Kleinian group of Hausdorff dimensions less than $1.$ In particular, we prove
that every convex cocompact Kleinian group of Hausdorff dimension $<1$ is a
classical Schottky group. This upper bound is sharp. The result implies that
the converse of Burside's conjecture \cite{Burside} is true: All non-classical
Schottky groups must have Hausdorff dimension $\ge1$. The prove of the theorem
relies on the result of Hou \cite{Hou}.
