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Abstract
Stellar pulsations, either as radial or nonradial dynamical variabilities, are found in many phases of stellar evolution, and these variable stars occupy vastly differing regions on the Hertzsprung-Russell diagram. The diagnostic potential of such oscillations is considerable and its importance will grow in the future when smaller and smaller amplitude variabilities can be monitored as a matter of routine. This review of the theoretical aspects of stellar pulsations appears in two parts. The first part introduces the theoretical concepts and the physical mechanisms involved in stellar pulsations and reviews recent advances therein. Applications of the theory to model neutron-star oscillations and the pulsations of hydrogen-deficient stars are also reviewed.