Intermodulation is a phenomenon occurring in nonlinear systems when excited at multiple frequencies. Intermodulation is often viewed as a negative effect, distorting the signal of interest. However, intermodulation can be turned into an advantage when probing nonlinear systems, and especially nonlinear resonators. One such system which we have studied is Atomic Force Microscopy (AFM) where a micro-cantilever with a sharp nanometer sized tip at one end is used to probe a surface. Conventional AFM methods can provide quantitative information on the surface topography but only qualitative information with respect to material contrast across the surface. By exciting the cantilever at two frequencies simultaneously, in what we call Intermodulation AFM, we measure up to 32 amplitude and phase images (in comparison to only one of each for conventional AFM). These additional observables provide increased contrast and can be used to quantitatively reconstruct the nonlinear tip-surface interaction which can then be related to material properties of the surface under investigation.