  We calculate the optical depth and the number of events due to gravitational
microlensing towards the Galactic bulge, the spiral arm directions $\gamma$
Scutum, $\beta$ Scutum, $\gamma$ Normae, $\vartheta$ Muscae and some dwarf
galaxies in the halo of the Galaxy. Using the events found by the MACHO
collaboration during their first year of observation towards Baade's Window we
estimate the mass functions for the bulge and disk populations following the
mass moment method. We find that the mass function can be described by a
decreasing power-law with slope $\alpha \simeq 2.0$ in both cases and a minimal
mass of $\sim 0.01$ $M_{\odot}$ for the bulge and $\sim 0.02$ $M_{\odot}$ for
the disk, respectively. Assuming that the obtained mass function for the disk
is also valid in the spiral arms, we find that the expected number of events
towards the spiral arms is in reasonable agreement with the observations.
However, the small number of observed events does not yet constrain much the
different parameters entering in the computation of the mass function. To study
the influence of the Magellanic Clouds on the shape and the velocity dispersion
in the halo we perform a N-body simulation. We find that their presence induces
a slight flattening of the halo ($q_{H}\simeq 0.8$). As a result the expected
number of microlensing events towards some targets in the halo, such as the LMC
or the SMC, decreases by about 20%, whereas due to the the modification induced
on the velocity dispersion the event duration increases.
