Scanning near-field acoustic microscopy (SNAM) is a new method for imaging the topography of nonconducting surfaces at a potential lateral resolution in the sub-micron range. The basic element of this method is a distance sensor consisting of a sharply pointed vibrating tip, which is part of a high-Q quartz resonator driven at its resonance frequency. The decrease of the resonance frequency or of the amplitude of vibration when an object comes into the proximity of the tip serves as the important signal. The dependence of this signal on pressure and composition of the coupling gas shows that the hydrodynamic forces in the gas are responsible for the coupling between object and tip. The sensor is incorporated into a scanning device. Well-resolved line scans of a grating of 8 μm periodicity, a lateral resolution of 3 μm and a vertical resolution of 5nm have been achieved in our first experiments.