The capabilities of the GAIA satellite for the detection of microlensing events are analyzed. The all-sky averaged photometric optical depth is ~7×10-8 and there are ~4000 photometric microlensing events during the five year mission lifetime. The all-sky averaged astrometric microlensing optical depth is ~5×10-5 and ~50 000 sources will have a significant variation of the centroid shift, together with a closest approach, during the mission lifetime. We show that GAIA is the first instrument with the capability to measure the mass locally in very faint objects like black holes and very cool white and brown dwarfs.