1. Introduction -- 2. Free oscillation of a uniform elastic sphere -- 3. Toroidal oscillation of a uniform shell -- 4. Toroidal and spheroidal free oscillations of a two-layered sphere -- 5. Oscillation of self-gravitating layered sphere -- 6. Calculation of eigenfrequencies and eigenfunctions for realistic earth-models -- 7. Effect of the earth's rotation on the eigenfrequencies of free oscillation -- 8. Asymptotic distribution of eigenfrequencies -- 9. Excitation of free oscillations in an elastic sphere -- 10. Recent and current research.