What is the function of the various brainwaves?

There are four brainwave states that range from the high amplitude, low frequency delta to the low amplitude, high frequency beta. 

These brainwave states range from deep dreamless sleep to high arousal. The same four brainwave states are common to the human species. They are consistent across cultures and country boundaries.

Read more in Scientific American:

 https://www.scientificamerican.com/article/what-is-the-function-of-t-1997-12-22/#:~:text=When%20the%20brain%20is%20aroused,of%20the%20four%20different%20brainwaves.&text=Alpha%20brainwaves%20are%20slower%2C%20and,to%2014%20cycles%20per%20second.