Matter-wave microscopy can be dated back to 1932 when Max Knoll and Ernst Ruska published the first image obtained with a beam of focussed electrons. In this paper a new step in the development of matter-wave microscopy is presented. We have created an instrument where a focussed beam of neutral, ground-state atoms (helium) is used to image a sample. We present the first 2D images obtained using this new technique. The imaged sample is a free-standing hexagonal copper grating (with a period of about 36 microm and rod thickness of about 8 microm). The images were obtained in transmission mode by scanning the focussed beam, which had a minimum spot size of about 2.0 microm in diameter (full width at half maximum) across the sample. The smallest focus achieved was 1.9 +/- 0.1 microm. The resolution for this experiment was limited by the speed ratio of the atomic beam through the chromatic aberrations of the zone plate that was used to focus. Ultimately the theoretical resolution limit is set by the wavelength of the probing particle. In praxis, the resolution is limited by the source and the focussing optics.