Very low mass stars and brown dwarfs are the most numerous stellar population in the Galaxy. Their observations have long been difficult (or even impossible) because oftheir very low luminosities. Recent instrumental progress (in particular on infrared detectors) have changed this situation. Two particulary important astrophysical issues need a good determination of the mass function (number of objects per mass interval): the influence of this population on Galactic dynamics, and the behaviour of the initial mass function at the bottom of the main sequence. These objects also severely test our understanding of the physics of degenerate objects and of dense cool stellar atmospheres dominated by molecular opacities. ln this thesis I have used DENIS (a Deep Near Infrared Southern sky survey) to determine the luminosity function (number of objects per luminosity interval) down to the bottom of the main sequence. During this work, one of the first two confirmed field brown dwarfs was discovered, and spectroscopically followed-up. To then derive the mass function, a binarity study is needed: 1° to correct the luminosity function for its binary bias, and 2° to obtain an accurate mass-Iuminosity relation. A systematic search for spectroscopie binaries was thus started during this thesis. It shows that the solar neighbourhood is still not weIl know: a significant number of companions remain unknow (11 are identified here), and distances to unrecognised binaries are underestimated. As an interesting byproduct of the stellar multiplicity study, we have obtained important information on stellar rotation at the bottom of the main sequence. We demonstrate that the time scale for angular momentum dissipation continues to increase with decreasing mass, to reach a few Gyr at spectral type M3-M4 (about 0.3 solar masses).
