May and might are literally synonymous, could means the ability to do something. I may/might study Latin. I could study Latin if I have time.

thanks a lot!))

I feel like may is much less common now. Especially for the use “I may go to the store” it’s much more common especially among young people to use might instead. May sounds more formal in a use like that.

May and might are very similar, but can be used in some different situations. For example, when asking for permission ("May I do something?") We only use may. When talking about future possibilities ("I might do it tomorrow" vs "I may do it tomorrow") it's used in the same way. Some people will tell you that "might" has a higher chance of happening than "may" (something like 50% vs 40% respectively) but not all native speakers will agree.