Back-rank mate
A castled king behind three unmoved pawns can be mated by a single rook. Learn to deliver it, and to avoid it.
A king with no air
Black's king is shut in by its own pawns. A rook or queen that reaches the back rank gives check, and the king has nowhere to go: f7, g7 and h7 are taken by its own pawns.
Deliver it
Your turn
Checkmate in one move.
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Rd8#. The pawns that shelter Black's king are what trap it.
Remove the guard
Your turn
Black's rook guards the back rank. Lure it away, then mate.
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Qb8+ forces Rxb8, and Rxb8# follows. A queen sacrifice is cheap when it leads to mate.
Giving the king air
Here Black has played ...h6 at some point. Step through the demo: Rd8+ is no longer mate, because the king escapes to h7. The flight square is called luft (German for air). One quiet pawn move ahead of time removes the danger.
Your own king
Question
Your king is on g1 behind pawns on f2, g2 and h2, the heavy pieces are being traded and your opponent still has a rook. What is a sensible precaution when you have a free move?
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Play h3 (or g3) to give the king a flight square
One tempo now means a back-rank check later is just a check.