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The aim of this thesis was to explore the statistical physics and the mechanical properties of individual biomolecules, to study their interactions, and to develop new techniques based on atomic force microscopy (AFM). First, we exploit the high resolution imaging of AFM over long DNA molecules adsorbed on a surface to measure the average end-to-end distance as a function of the DNA length, along with its full distribution function. The latter is almost never determined experimentally, and is not available with ensemble techniques, such as light scattering. We found that the scaling exponents are closer to the values predicted by the polymer theory for a 3D self-avoiding random walk (SAW) than for a 2D SAW. These results suggest that the adsorption process of the DNA molecules is akin to a geometric projection from 3D to 2D, known to preserve the scaling properties of fractal objects of dimension df < 2. Second, taking advantage of the possibility of AFM to also manipulate biomolecules, we investigate the specific interactions between the glycoprotein avidin and the vitamin biotin, the ribonuclease barnase and its inhibitor barstar, and the West Nile Virus surface glycoprotein E and the laminin binding protein. The dependence of the most probable unbinding force on the force loading rate has revealed details of the energy landscapes of the unbinding process of these highly efficient and specific interactions. Beside this standard method, we have measured the lifetime of the avidin-biotin bond, kept stretched at a constant force, as a function of this force, and combined this approach with a small dithering of the AFM tip in order to further explore the avidin-biotin energy landscape. Finally, the viscoelastic properties of biomolecules, such as dextran and titin, have been studied using standard force spectroscopy combined with a small oscillation of the AFM tip. A theoretical description for excitation frequencies near the first and the second resonance of the cantilever has been developed to be able to extract, from the amplitude and phase measurement of the oscillations, the stiffness and friction coefficients of the biomolecule being stretched. We conclude that an excitation frequency of 3 kHz gives reliable results for the stiffness measurement whereas frequencies of 15-25 kHz are more appropriate for the dissipation measurements.