Abstract
We give a global (classical) description of the family of BTZ multi black-holes, including the spinning case, as quotients of open domains of the anti-de Sitter space (AdS) by discrete groups of isometries. Fixing the topology, and fixing the mass and angular momenta, this family is parametrized by the pairs of elements of the Teichm\"{u}ller space of a given Rieman surface with prescribed holonomy on the boundary.