These are a bunch of fast solution methods I've developed over time. I've attached some descriptions of the steps and their history, as well as pictures showing what part of the cube gets solved when. A bit of advanced knowledge might be required, since these articles are really intended more for people seeking to learn an interesting new method, rather than people trying to solve the puzzle for the first time.
- Sortega (2x2x2) - a bit of a hybrid between Guimond and Ortega, which lets you solve almost all of the cube with only R and U moves
- Triangular Francisco (3x3x3) - a method starting with a triangle, fast enough to be sub-20 and quite different from most major methods
- Tripod (3x3x3) - intuitive blockbuilding until the last 5 pieces
- Columns First (4x4x4 and 5x5x5) - very few slice moves, and very few x/z rotations after the first center
- Optimized Blockbuilding LBL (4x4x4 and 5x5x5) - roughly based on a layer-by-layer method, but much much faster than those methods usually are
- Half Backbone (Pyraminx) - 3-step method with 5 algorithms
I've decided to host descriptions of a few other methods, too. These aren't by me (although I might have contributed a few optimizations) but they didn't seem to be very well explained anywhere else.