"The revealed the to have an unexpected richness of structure. Many of the observed features have now been identified as collective effects arising from the of the ring material. These effects include , the main topics of this review chapter. Both kinds of waves were first discussed in the astronomical literature in connection with the dynamics and structure of , and our discussion contrasts the similarities and differences between the and s. After developing the theory of free and forced waves of both types, we discuss how the observed waves can be used as diagnostics to obtain crucial parameters that characterize the physical state of the rings."