Take a look at my bachelor thesis (written in German), done some time ago, but still of importance for SkewbSkills! Access it here via my personal website hosted at CERN.

In the document, you'll find the derivation of the Cube & the Skewb Group, using notions and theorems of Algebra (mostly Group Theory). In particular, knowing which pieces are permuted for which move and how you can identify them was essential to get the correct scramble images automatically without storing any picture!