As far as I know his method is the only fast solution that does not involve a large amount of memorisation. I mostly use his method to solve the cube's final layer. Below is a corners first algorithm, i.e. all the corners are solved first, then the edges. This kind of solution is relatively easy to understand and remember. They can be quite fast because of this, but they do generally use more moves than layer methods because turns of a slice are often counted as two moves.
Corners then edges.
Use any method you like. Use part of solution 1, or use the method for the mini cube. Afterwards the top and bottom centres should match their corners, but the centres in the middle layer need not match. Find the edge piece that belongs at the front top. Hold the cube with the destination of the piece at the front top and turn M to bring the piece to the back right.