GAIA is the “ super-Hipparcos ” survey satellite selected as a Cornerstone 6 mission by the European Space Agency . GAIA can measure microlensing by the brightening of source stars . For the broad G band photometer , the all-sky source-averaged photometric optical depth is \sim 10 ^ { -7 } . There are \sim 1300 photometric microlensing events for which GAIA will measure at least one datapoint on the amplified lightcurve . GAIA can also measure microlensing by the small excursions of the light centroid that occur during events . The all-sky source-averaged astrometric microlensing optical depth is \sim 2.5 \times 10 ^ { -5 } . Some \sim 25000 sources will have a significant variation of the centroid shift , together with a closest approach , during the lifetime of the mission . This is not the actual number of events that can be extracted from the GAIA dataset , as the false detection rate has not been assessed . A covariance analysis is used to study the propagation of errors and the estimation of parameters from realistic sampling of the GAIA datastream of transits in the along-scan direction during microlensing events . The mass of the lens can be calculated to good accuracy if the lens is nearby so that angular Einstein radius \theta _ { E } is large ; if the Einstein radius projected onto the observer plane { { \tilde { r } } _ { E } } is about an astronomical unit ; if the duration of the astrometric event is long ( \mathrel { \hbox to 0.0 pt { \lower 3.0 pt \hbox { $ \sim$ } \hss } \raise 2.0 pt \hbox { $ > $ } } 1 year ) or if the source star is bright . Monte Carlo simulations are used to study the \sim 2500 events for which the mass can be recovered with an error of < 50 \% . These high quality events are dominated by disk lenses within a few tens of parsecs and source stars within a few hundred parsecs . We show that the local mass function can be recovered from the high quality sample to good accuracy . GAIA is the first instrument with the capabilities of measuring the mass locally in very faint objects like black holes and very cool white and brown dwarfs . For only \sim 5 \% of all astrometric events will GAIA record even one photometric datapoint . There is a need for a dedicated telescope that densely samples the Galactic Centre and spiral arms , as this can improve the accuracy of parameter estimation by a factor of \sim 10 . The total number of sources that have an astrometric microlensing variation exceeding the mission target accuracy is \sim 10 ^ { 5 } . The positional measurement of one source in every twenty thousand is affected by microlensing noise at any instant . We show that microlensing is negligible as an unbiased random error source for GAIA .