Atomic Force Microscopy (AFM) is a powerful tool for mapping the topography of a wide variety of surfaces at the nanometer scale, from insulators to conductors, both soft and hard matter. Beyond topography mapping, the surface analysis power of the AFM lies in it's ability to measure

tip- surface forces. Today such force measurements are done in a quasi-static way. However, the most sensitive AFM imaging methods are dynamic techniques which exploit a cantilever resonance. Presently there is great interest in the AFM community to develop dynamic AFM methods which can extract the tip-surface forces.  I will discuss these developments and our solution to this problem, which is based on the intermodulation of two pure drive tones.  When the linearity of the oscillating cantilever is perturbed by the nonlinear tip-surface forces, an intermodulation spectrum is generated in cantilever response.  A perturbation analysis of of the nonlinear oscillator shows how this spectrum contains the information needed to extract the nonlinear tip-surface force.