We present a geometrical description of the space of density states of a
quantum system of finite dimension. After presenting a brief summary of the
geometrical formulation of Quantum Mechanics, we proceed to describe the space
of density states \D(\Hil) from a geometrical perspective identifying the
stratification associated to the natural GL(\Hil)--action on \D(\Hil) and
some of its properties. We apply this construction to the cases of quantum
systems of two and three levels.Comment: Amslatex, 18 pages, 4 figure
