Abstract: The invention relates to a device for polishing hard surfaces, especially glass surfaces, said device comprising polishing system (5) provided with a replaceable polishing disk (6). Said polishing system (5) can be displaced in a two-dimensional manner by means of a displacement device (10) comprising a holding element (11) for the polishing system (5), and guiding elements (12, 18; 20, 25) for displacing the holding element (11) in XY directions. The inventive device enables hard surfaces to be repaired in a simple and precise manner.