  We study codimension one holomorphic distributions on the projective
three-space, analyzing the properties of their singular schemes and tangent
sheaves. In particular, we provide a classification of codimension one
distributions of degree at most 2 with locally free tangent sheaves, and show
that codimension one distributions of arbitrary degree with only isolated
singularities have stable tangent sheaves. Furthermore, we describe the moduli
space of distributions in terms of Grothendieck's Quot-scheme for the tangent
bundle. In certain cases, we show that the moduli space of codimension one
distributions on the projective space is an irreducible, nonsingular
quasi-projective variety. Finally, we prove that every rational foliation, and
certain logarithmic foliations have stable tangent sheaves.
