Abstract : The nature of the dark matter is a major question in cosmology today. A plausible hypothesis is that the dark matter is composed partly of ordinary baryons in the form of MAssive Compact Halo Objects, or "MACHOs", which reside in galactic halos. To detect such objects, one may search for the effects of graviational microlensing that are produced when a MACHO passes in front of a more distant star. The AGAPE collaboration is carrying out this search in the direction of M31, the Andromeda galaxy, about 725 kpc away. At this distance, very few stars are resolved, which is why AGAPE had to design and put into practice a method of analysis, called "pixel lensing", that allows the detection of flux variations directly in the pixels of the CCD camera.
The POINT-AGAPE collaboration observed M31 from 1999 to 2002 using the 2.5 m Isaac Newton Telescope (INT), at La Palma in the Canary Islands, and employing the wide-field camera (WFC) to image two fields, each 0.3 deg$^2$. This thesis concerns the analysis of the data obtained during the first two seasons of observation (August 1999 to January 2001). About 10 microlensing candidates were detected. For the majority, source-star variability is the likely explanation for the events. This hypothesis will be better constrained when the final season's data are analyzed. Four microlensing candidates are, however, especially worthy of notice because they took place on time scales of only a few days, and it is therefore particularly difficult to think of an alternatively interpretation to microlensing.
For two of the four candidates, self-lensing (in which the lenses are themselves M31 stars that lie in front of the M31 sources) is the most plausible hypothesis since the events lie projected close to the M31 bulge. A third candidate lies 2'54'' from the center of M32, a dwarf elliptical satellite galaxy of M31. If M32 lies in front of M31, the optical depth is most likely dominated at this position by events having a source in the M31 disk lensed by either a MACHO or an M32 star. The last candidate is a star in the M31 disk lensed by either a MACHO or another star in the disk of M31. Although the latter possibility is less likely, it is not ruled out. Regardless, the number of detected events is much less than what is predicted by Monte Carlo simulations of the experiment, even if the halo contains no MACHOs. This shows that either there is a poorly understood bias in the detection efficiency or the models (luminosity function, density profile, etc) used in the simulations require revision. The former possibility is under investigation.