Commutators are a systematic method to craft algorithms to solve the Rubik's Cube born out of the concept from abstract algebra of the same name.
They take the form of [P, Q] = P·Q·P'·Q' where P and Q are two sequences of moves and P' and Q' are their inverses, respectively.
I've provided commutators and their component sequences here to:
With just these four algorithms you will be able to solve a Rubik's Cube and hopefully gain a better understanding of its inner workings.
With practice, you will be able to extrapolate this process to solve other twisty puzzles as well 👍