Learn · Level 3 · the first two layers
The 41 pairs
Speed on the first two layers comes from seeing a corner and its edge as one thing: a pair with 41 possible starting positions and a known route home from each. This is where most of a solve's time is won.
Level 1 placed corners and edges one at a time. F2L, first two layers, does both at once: find the corner and the edge that belong together, bring them side by side in the top layer, and lower them into their slot as a unit.
Most of these cases are not memorised. Solvers learn the four basic inserts, then work out the rest by hand, and only later polish the stubborn ones with algorithms. Read the diagrams that way: grey pieces do not matter, coloured pieces are the pair and its landing ground, and the white outline marks the pair.
Basic inserts
Reposition the edge
Flip the corner
Split the pair
Pair on the side
The strange pair
Corner in its slot
Edge in its slot
Both in the slot
Checked by simulation before publishing: the position shown plus the moves shown must produce a finished cube, and the algorithm must touch nothing outside its own job. The diagram and the player are drawn from the same simulated position, so they cannot disagree. Completeness is checked by enumeration: up to a turn of the top layer, the 41 definitions cover every position a pair can occupy, each exactly once.