Guidance on creating algs

I was a hardcore cuber for a good 3-4 years but then I left it behind and just recently picked it up when studying a Bachelor in math. I purchased some cubes and started cubing again, but I wanted to start creating my own algorithms. It's been hard to find where to start, I see everyone throwing around the idea of "commutators" and it seems super reasonable on normal cubes and I created my own algs to solve 3x3, but I wanted to take this up a bit and got a 4x4x4 mixup and I want to create my own solutions but I've been struggling on creating algs for bringing the cube back to a cube-state, and if by random chance I end up on cube state, I struggle to create algs for solving parities or weird states. Any guidance on this? I want to learn and create my own solutions and not watch tutorials, but I'm struggling to fully understand the idea of these types of processes for cubes that change shapes. I also recently bought some Traiphum cubes and I would want to be able to solve those with my own methods as well. Any guidance on how to start and where to approach these types of cubes?