  We study the BPS black hole solutions of the (truncated) action for heterotic
string theory compactified on a six-torus. The O(3,Z) duality symmetry of the
theory, together with the bound state interpretation of extreme black holes, is
used to generate the whole spectrum of the solutions. The corresponding
spacetime structures, written in terms of the string metric, are analyzed in
detail. In particular, we show that only the elementary solutions present naked
singularities. The bound states have either null singularities (electric
solutions) or are regular (magnetic or dyonic solutions) with near-horizon
geometries given by the product of two 2d spaces of constant curvature. The
behavior of some of these solutions as supersymmetric attractors is discussed.
We also show that our approach is very useful to understand some of the
puzzling features of charged black hole solutions in string theory.
