Alchemists Guilds were a major part of Aerum society before The Withering took hold. Not much is currently known about the guilds, as they disappeared when the Aerum fled The Withering. It is known that they used Alchemy for many things, like heating and lighting, and the skills were passed down from master to student.
Everheart Alchemists
The members of the Everheart Alchemists Guild were the caretakers of the Evertree and were the most deeply connected to the Song of Myora. The Apprentice is the only remaining Aerum member of this guild. The two constructs, Book and Coppertop mentor the Apprentice in Alchemy in the hopes that they will be able to save the Evertree.
The Everheart Alchemists became the Tree's custodians, working to keep the Tree healthy, and mantaining harmony between the people and the land.
Other Alchemists Guilds
It is currently unknown exactly how many guilds there were or what their individual purposes might have been. When the Everheart Alchemists Guild attempted to warn them about the overuse of Alchemy, the other Guilds refused to listen. Upon entering the first Vault, Coppertop makes a comment suggesting that the Vaults were constructed by the guilds, potentially with the aim to hide the song fragments that they held.