Gravitational microlensing by the dark halo of M31

It has been shown by Paczy\'nski that gravitational microlensing is potentially a useful method for detecting the dark constituents of the halo of our galaxy, if their mass lies in the approximate domain $10^{-6}<M/M_\odot<10^{-1}$. Microlensing observations now im progress monitor several millions of stars in the Large Magellanic Cloud and in the Galactic Bulge. Here I discuss the main features of the microlensing events: in particular their rates and probability.