In recent years, astronomers have witnessed major progresses in the field of
stellar physics. This was made possible thanks to the combination of a solid
theoretical understanding of the phenomena of stellar pulsations and the
availability of a tremendous amount of exquisite space-based asteroseismic
data. In this context, this chapter reviews the basic theory of stellar
pulsations, considering small, adiabatic perturbations to a static, spherically
symmetric equilibrium. It starts with a brief discussion of the solar
oscillation spectrum, followed by the setting of the theoretical problem,
including the presentation of the equations of hydrodynamics, their
perturbation, and a discussion of the functional form of the solutions.
Emphasis is put on the physical properties of the different types of modes, in
particular acoustic (p-) and gravity (g-) modes and their propagation cavities.
The surface (f-) mode solutions are also discussed. While not attempting to be
comprehensive, it is hoped that the summary presented in this chapter addresses
the most important theoretical aspects that are required for a solid start in
stellar pulsations research.Comment: Lecture presented at the IVth Azores International Advanced School in
Space Sciences on "Asteroseismology and Exoplanets: Listening to the Stars
and Searching for New Worlds" (arXiv:1709.00645), which took place in Horta,
Azores Islands, Portugal in July 201