This book surveys the physics of small clusters of particles undergoing oscillations and vibrations. These oscillations occur in nuclear physics and the physics and chemistry of atomic clusters. First, the authors survey experimental information on collective vibrations in atoms, metal clusters and nuclei, then they develop theoretical tools to understand these findings. Finally, they discuss important vibrational modes observed in the different systems and mechanisms for the damping of vibrational modes and the effects of excitation energy on the modes.