[zwegner]

There's a method entirely based on group theory, a version of the original computer algorithm created to solve the cube (the Thistlewaite algorithm) simplified for use by a human [1]. It iteratively solves the cube into simpler groups that need a smaller moveset to solve (the last step uses only half turns on each face, no quarter turns). It requires only a bit of memorization, and you can understand exactly how the algorithm works. It's not a great speedsolving method, but you can get relatively fast with it: in [2] there's a solve below 30 seconds.

[1] https://www.ryanheise.com/cube/human_thistlethwaite_algorith... [2] https://www.youtube.com/watch?v=GmjYWYDPhiM