Ab initio calculations were used to determine physical properties of AlN(0001) surface under Al coverage. It was shown that Al atoms are adsorbed in T4 sites for very low Al coverage, up to θAl=1/4 monolayers (ML). For higher Al coverage, θAl=1/4ML up to θAl=1ML the adlayer becomes disordered and corrugated vertically. In this coverage range (0<θAl≤1ML) the Al bonding energy is independent on the coverage and equal to EadsDFT≅5.0eV. For higher coverage, 1ML≤θAl≤7/6ML, the Al adlayer becomes ordered and atomically flat. The Al adsorption energy in this range is EadsDFT≈6.0eV, i.e. much higher. For higher coverage, θAl>1.25ML, the Al adatoms are located in the second layer. The adsorption energy is reduced to EadsDFT=3.97eV at θAl=1.25ML and linearly increasing to EadsDFT=4.88eV for the coverage increase up to θAl=2ML. Full thermodynamic analysis identified two regions in equilibrium with Al vapor: first at very low pressures where θAl≤10-3ML and the second for higher pressures which is 1ML≤θAl≤7/6ML. The second region is relevant for physical vapor transport (PVT) AlN growth. The nitrogen adsorption process, important for PVT AlN growth, takes place at single or double Al layer covered AlN(0001) surface.