Rubik's Cube algorithms, with pictures you can read.

What algorithms are

An algorithm is a fixed list of moves that changes a few pieces and leaves the rest alone. Cubers write algorithms in notation, memorise them and use them whenever the same pattern appears. The last layer has a small number of patterns, so a small number of algorithms covers every cube you will ever meet.

In the CFOP method the last layer is solved in two stages: OLL turns the pieces so the top face is all yellow, and PLL moves them into place. In two-look versions you split each stage in two, so that you only need a handful of algorithms at first.

A sensible order to learn them

1. Finish the seven-step beginner method a few times.
2. Learn two-look OLL: the cross algorithm, then Sune, Anti-Sune and the other corner cases.
3. Learn two-look PLL: the A-perm, then the U-perms, H and Z.
4. Add the rest of PLL a few at a time, starting with the T-perm and Y-perm.
5. Time yourself with the cube timer and watch your Ao5 fall.

Useful short sequences

• The sexy move: R U R' U'
• The sledgehammer: R' F R F'
• Edge insert (right): U R U' R' U' F' U F
• Edge insert (left): U' L' U L U F U' F'
• Corner cycle: U R U' L' U R' U' L
• Edge swap: R U R' U R U2 R' U
• Corner twist: R' D' R D

These small triggers appear inside many longer algorithms. Recognising them makes a long algorithm easier to remember, because you only have to learn which triggers go in which order.