From 1d4chan

"Readers will notice a thematic resemblance between the aboleths, the Elder Evils, and various creatures or beings found in the stories of H. P. Lovecraft. This is, of course, completely intentional. Of all the major aberration races in the DUNGEONS & DRAGONS game, the aboleths best personify the sense of cosmic horror and the ultimate insignificance of humankind expressed in Lovecraft’s writings. In fact, it’s quite easy to treat the aboleths themselves as a Lovecraftian race akin to the elder things featured in “At the Mountains of Madness” and “The Dreams in the Witch House.”"

– Lords of Madness

Aboleth are aquatic aberrations with impressive psionic abilities (or magic, depending on edition). Can Dominate, as well as force you to lose the ability to breath air. Creators of the Skum, descendants of humanoid slaves that are enthralled to the aboleth. Also, their species is older than the world and the gods themselves, and they can back up that claim thanks to their ancestral memory, meaning that they are incapable of forgetting and all their memories are passed down from parent to offspring. They can also absorb the memories of anything they eat. The only thing they don't recall is the genesis of the mind flayer species (since they're from the distant future) so of course this freaks the aboleths out a little bit since they have no idea where the fuck they came from.

They first appeared in the Dwellers of the Forbidden City adventure module in 1980-81, and then in Monster Manual II a few years later. Dragon Magazine #131 has an article called Ecology of the Aboleth. The normal aboleth are merely well... normal. There are larger and more powerful aboleth. With psychic abilities that would put The Emperor and Professor X to shame. Mother Brain aint got SHIT on the most powerful one. Sadly this article has seemed to have been ignored by everything that came after it, even though 2nd edition had some fantastic campaign and lore books for a lot of races. Lords of Madness introduced a few new kinds of Aboleths and also contained some great lore on them. An amphibious aboleth is an aboleth that has adapted to be able to live both in and out of water, at the cost of not being as good at swimming. Uobilyths are aboleths don't live in water at all and can fly, and also are never lawful aligned. Stygian aboleths are aboleths that have been mutated as a result of living a long time in Stygia. Most aboleths do not worship gods, but do pay respects to five beings known as the Elder Evils.

Unlike the beholder and illithid, aboleth are OGL content. For this reason, Pathfinder uses them as the main shadowy, manipulative aberration with innate mind control magic. In fact, Pathfinder aboleths are just the most common member of a whole family of psychic fish monsters known collectively as alghollthus (If you look at the gallery below you can see they ran out of design ideas and just started to put red eyes on random aquatic animals). Aboleths have also been renamed Alghollthu Masters in Pathfinder 2e, just in case WotC decides to copyright the name.