Dissolution processes on three low index faces of anhydrite (CaSO4) crystal in water were monitored in situ with atomic force microscopy. Well-controlled layer-by-layer dissolution was observed on the most stable (010) surface, where rectangular pits with monolayer depth grew in the directions of the crystal axes until they met each other forming an atom-hat surface, The shape of the pits suggests that the dissolution proceeds row by row, by formation of vacancies at the step edge followed by rapid removal of kink ions. Speeds of the step retreat decreased markedly when sulfate and calcium ions were added to water. The steps got saturated at different concentrations. Stabilities of the steps are discussed in relation to the ionic arrangement. On a highly directional (100) face, marked anisotropy was observed in step stabilities. in addition to the numbers of ionic bonds and charge neutrality as a whole, local polarity greatly affects the stabilities of the step structures. The speeds of the step retreat vary by five orders of magnitude depending on the structures, but they all approach zero toward the bulk saturation concentration of CaSO, in water.