Grand canonical Monte Carlo calculations are employed to investigate water adsorption on kaolinite at 298 and 235 K. Both basal planes (the Al and Si surfaces) as well as two edge-like surfaces are considered. The general force field CLAYFF is used together with the SPCIE and TIP5P-E models for water. Problems that occur in single slab simulations due to arbitrary truncation of the point charge lattice are identified, and a working remedy is discussed. The edges and the Al surface adsorb water at subsaturation in the atmospherically relevant pressure range. The Si surface remains dry up to saturation. Both edges have a very strong affinity for water and adsorb continuously up to monolayer coverage. The Al surface has a weaker affinity for water but forms a subsaturation monolayer. On the Al surface, the monolayer is formed in an essentially sharp transition, and strong hysteresis is observed upon desorption. This indicates collective behavior among the water molecules which is not present for the edges. Binding energies of singly adsorbed water molecules at 10 K were determined to understand the differences in water uptake by the four kaolinite surfaces. Binding energies (SPC/E) of -21.6, -46.4, -73.5, and -94.1 kJ/mol, were determined for the Si surface, Al surface, unprotonated edge, and protonated edge, respectively. The water monolayer on the Al surface, particularly at 235 K, exhibits hexagonal patterns. However, the associated lattice parameters are not compatible with ice 1h. Water density and hydrogen bonding in the monolayers at both 298 and 235 K were also determined to better understand the structure of the adsorbed water.