Lesson
White to move. Main line: 1. Ra8#
The white king on g6 already covers g7, h7 and g8 — the king’s only escape squares. So 1.Ra8# gives check along the eighth rank with nowhere to run: checkmate.
Every player must know the king-and-rook mate cold. The method is always the same: the king takes the escape squares away, the rook delivers the check from a safe distance. Master it here, then practise driving the king to the edge.
Getting to this position is the real skill. Cut the king off along a rank or file with the rook, walk your own king up to face it, and shrink the box one line at a time. The check comes only when the defending king has run out of room to be pushed into.