The central aim of this thesis is to give further insights into the structural properties of the calcite(104) surface and especially to unravel its surface reconstruction by clarifying the contradicting reports of the (2 × 1) and row-pairing reconstruction. Within this thesis, the pristine as well as the CO and H2O-covered calcite(104) surface is investigated for the first time with non-contact atomic force microscopy (NC-AFM) operated at 5 K. CO terminated tips are used in the measurements to benefit from the improved contrast capabilities and detailed understanding of contrast formation with these tips.