Internal waves:
-P-waves: primary waves because they are the first to arrive at a seismograph. They are compressive-type waves and cross the planet via solid, gas, or liquid.
-S-waves: secondary waves. They are transversal-type and their vibration is perpendicular to their movement and propagation. They can't cross through the Earth's nucleus.
Superficial waves:
-L-waves: love waves. They travel above the Earth from side to side, as a result of the interference of multiple S-waves propagated on a superficial elastic layer.
-R-waves: Rayleigh waves, they're a superficial acoustic type of wave that travels along the surface of solids.