P waves, otherwise known as primary waves, are the first kind of body wave to occur during an earthquake. This is because P waves travel faster than other kinds of seismic waves. P waves are sometimes called compressional waves because they compress the ground in front of them just as sound waves compress air. Anything that is in the path of a P wave will be pushed and pulled in such a way that it will move in the same direction as the wave's propagation. Although P waves move very quickly, they are not particularly damaging. In fact, most people don't even notice them. However, animals can sometimes detect P waves. This is why dogs often start barking before an earthquake begins to become noticeable to humans.
S waves, otherwise known as secondary waves, are the second kind of body wave to occur during an earthquake. S waves travel more slowly than P waves. S waves move through rock but not through fluids, such as a body of water. Anything solid that is in the path of an S wave will move in a direction perpendicular to the S wave's propagation.
The fastest kind of surface wave is called a Love wave. This type of wave is named after A. E. H. Love, the mathematician who figured out how to model these waves in the early 20th century. Ground material subject to Love waves moves horizontally along the surface of the earth, much as a snake does.
A slower kind of surface wave is the Rayleigh wave. It is named after Lord Rayleigh, who postulated in the late 19th century that this type of wave must exist. Although Rayleigh waves move more slowly than Love waves, they are much more damaging than the other three types of waves. Unlike Love waves, Rayleigh waves move the ground both vertically and horizontally along the direction of wave motion. In addition, Rayleigh waves tend to be noticeably larger than other wave types. As a result, most of the destruction caused by earthquakes stems from Rayleigh waves.