Rook vs Pawn Endgames
Rook vs a single pawn, seemingly simple, but the positions that arise when the pawn reaches the 6th or 7th rank are subtle and critical. The outcome often depends on a single tempo: whether the rook can get behind the pawn, and whether the defending king is cut off.
Rook behind the pawn
Tarrasch's rule: "Rooks belong behind passed pawns." When the rook is behind the pawn, the rook gains freedom as the pawn advances, each step forward gives the rook more squares. When the rook is in front of the pawn, the rook loses squares as the pawn advances. See rook endgames.
Critical positions
The Lucena position (rook + pawn vs rook): winning with the "bridge" technique. The Philidor position: the standard drawing method, rook on the 6th rank, then checking from behind.
Training
Practise R vs P positions against the computer. Memorise the Lucena bridge and Philidor defence until they're automatic.