An Abelian Group, in the simplest terms, is a set of elements with a certain je ne sais what. But don't just take my word for it, let's dive into the details.
Definition: A set G is called an Abelian Group, if it has a binary operation "ยท" (read: dot-dot) with certain properties: closure, associativity, identity, and invertibility. Sounds like a party, right?