We report the measurement of infrared transmission of large C60 single crystals. The spectra exhibit a very rich structure with over 180 vibrational absorptions visible in the 100 -4000 cm range. Many silent modes are observed to have become weakly IR active. We also observe a large number of higher order combination modes. The temperature (77 -300 K) and pressure (0 -25 kbar) dependences of these modes were measured and are presented. Careful analysis of the IR spectra, in conjunction with Raman scattering data showing second-order modes and neutron scattering data, allows the selection of the 46 vibrational modes of C60. We are able to fit all of the Srst-and second-order data seen in the present IR spectra and the previously published Raman data ( 300 lines total), using these 46 modes and their group-theory-allowed second-order combinations.