Groups are an incredibly powerful tool where you consider a set of elements connected by one or more binary operations. The beauty of groups is that, instead of using the operations directly, we abstract them away and use the theory of groups to find results. Provided an operation satisfies the group axioms, it doesn't matter how that operation is defined or how complicated it is - we can prove results using only the abstract concept of an operation (this will make more sense, I promise).
is a set
with a binary operation that satisfies the following axioms: