Terahertz laser VRT spectra of the water dimer consisting of 731 transitions measured with an average precision of 2 MHz and involving four (D2O)(2) intermolecular vibrations (one previously published) have been measured between 65 and 104 cm(-1). The precisely determined energy level patterns differ both qualitatively and quantitatively from the predictions of several dimer potentials tested, and reveal an ordering of the intermolecular vibrations which differs dramatically from that predicted by standard normal mode analysis. Strong coupling is indicated between the low barrier tunneling motions and the intermolecular vibrations as well as among different vibrations. Particularly, the 83 cm(-1) (acceptor wag) and 90 cm(-1) (D2O)(2) (acceptor twist) vibrations interact through a Coriolis perturbation. These spectra provide the basis for our recent determination of the water pair potential. The corresponding data set for (H2O)(2) is presented in an accompanying paper.