  Let X be an analytic vector field defined in a real analytic manifold of
dimension three. We prove that all the singularities of X can be made
elementary by a finite number of blowing-ups in the ambient space.
  New version: Some misprints have been corrected and the text have been
slightly reorganized. The final version appears in Acta Mathematica -Volume
197, Number 2, 167-289.
