First- and second-order perturbation methods for small amplitudes have been used to obtain periodic solutions to the modified Rayleigh equation that are applicable to the adiabatic pulsation of bubbles in liquids. It is demonstrated theoretically that bubble pulsation is a damped oscillation whose fundamental frequency is a function not only of hydrostatic pressure and surface tension, but also of liquid viscosity, and that integral overtones of the fundamental may exist at large amplitudes. A theory of vibration-induced cavitation is presented in which the Rayleigh equation is transformed into an equivalent Mathieu equation for small radial motions. The onset of cavitation at small pressure amplitudes is found to be a sharp function of frequency, bubble radius, and hydrostatic pressure, and it is shown that there is a frequency and bubble size above and below which, respectively, cavitation will not occur. Applications of bubble pulsation and cavitation phenomena to pumping and mass transfer operations are discussed.