The vibrational frequencies and electric polarizability of the C-60 molecule, both in the gaseous and in the solid phases, are calculated from first principles using density-functional perturbation theory. This method also allows us-to obtain the infrared and Raman activities which had never been calculated before. Our results are In excellent agreement with-existing experimental data, and they provide accurate predictions for those quantities (such as silent-mode frquencies and vibrational eigenvectors) which are not easily accessible to experiments.