1. Introduction -- 2. Basic wave propagation -- 3. Transforms -- 4. Review of continuum mechanics and elastic waves -- 5. Asymptotic ray theory -- 6. Rays at an interface -- 7. Differential systems for stratified media -- 8. Inverse transforms for stratified media -- 9. Canonical signals -- 10. Generalizations of ray theory -- App. A. Useful integrals -- App. B. Useful Fourier transforms -- App. C. Ordinary differential equations -- App. D. Saddle-point methods.