This solution method is designed to solve Rubik's cube and to solve it quickly, efficiently, and without having to memorize a lot of sequences. For ease and speed of execution, turns are mostly restricted to the top, right, and front faces, and center and middle slices. Strong preference is given to the right face, since it is one of the easiest faces to turn for many people. Yet all sequences are minimal (or very close to minimal) by the slice-turn metric.
For an introduction to the notation used in this page, go to the cube concepts page.
This solution method orients cubies before positioning them. The idea is that it is easier to permute cubies after they've been oriented than before orienting them, because once the cubies have been oriented, the facelet colors that determine their permutation make easily identifiable patterns on the cube. Orienting cubies, whether done before or after positioning them, is always easy because orientation requires focusing on only one face color and on the patterns that that color makes on the cube. For middle-slice edges on the last layer, permuting cubies after they've been oriented is a very simple affair, thus reinforcing this principle.
Do not worry about centers or edges while solving corners. Position centers while beginning to solve edges. You really only need to position top and bottom centers at that point, but positioning all centers may make things easier for you. Middle-slice centers will be positioned along with middle-slice edges on the last step.
This solution method is based on Minh Thai's Winning Solution. Ideas and sequences are borrowed from other solution methods, and appropriate attributions are made in those sections.
Go to Solving Corners to continue.