F2L or First Two Layers is the second step of the CFOP method, which aims to solve the first two bottom layers of a 3x3. Each algorithm solves a pair (an edge and a corner) into their designated location.
Each case is recognized by the position and orientation of the two pieces in relation to the target slot. Since there are four possible target slots, each case has four variants to avoid rotations.
The basic 41 cases deal with all permutations where the two pair pieces are on the U layer and/or in the target slot.
Try to learn each case intuitively, understand how the pieces interact and inserted. It will be easier to memorize and utilize on different slots.
Most of the cases can be solved without a rotation, while the rest are solved with a single rotation. If you do rotate, prefer to do so in a way that the destination slot will be in the back - leaving you with the two front slots visible.
Recognising cases is just as important as remembering the alg to solve it : this is why we group the cases by shapes. It is also good to learn them this way. If you prefer, you can group them together by type of moves (e.g. Sune-like, R U2 R’, etc.). Use the “bookmarks” buttons to build your own sheets and groups.