This chapter serves as an introduction to theoretical seismology. The seismic body waves, seismic surface waves, seismic ray theory, and the free oscillations of the Earth are formulated systematically based on respective adequate models of the Earth. Particular emphasis is dedicated to the free oscillations. First, the ordinary differential equations of the free oscillation of the spherical Earth model taking into account of the Coriolis force are derived in detail. Second, a perturbation theory of the free oscillation is provided in detail. These are usually not found in introductory books. The relations among the free oscillation theory, surface wave theory, and body wave theory are also formulated. Finally, the determination of the Earth’s internal structure and physical parameters using astro-geodetic data, seismic body wave data, and free oscillation data are summarized, including a discussion on the stratification within the Earth.