We present the first pair plus three-body potential of water from ab initio calculations that quantitatively reproduces the experimental far-infrared spectra of the water dimer and trimer. The dimer spectrum was obtained from the pair potential through rigorous six-dimensional quantum calculations of the vibration- rotation-tunneling levels. The three-body interactions, together with the pair potential, produce an accurate representation of the hydrogen bond torsional levels of the water trimer.