The document discusses different types of waves including transverse waves, longitudinal waves, water waves, and Rayleigh surface waves. Transverse waves involve particles oscillating perpendicular to the direction of wave propagation. Longitudinal waves involve particles oscillating parallel to the direction of propagation. Water waves and Rayleigh surface waves involve a combination of both transverse and longitudinal motion. Rayleigh surface waves cause the most damage in earthquakes and involve both up-down and side-to-side particle motion.