En passant is a special pawn capture in chess. When a pawn moves two squares forward from its starting position and lands directly beside an enemy pawn, that enemy pawn may capture it as if it had only moved one square. The capture is only legal on the very next move. It is the only capture in chess where the capturing piece does not end up on the square of the piece it captured.
All three must be true at the same time. If any one of them fails, the capture is not legal.
Your pawn moves diagonally forward one square, onto the square the enemy pawn passed over rather than the square it is standing on. The enemy pawn is then removed from the board.
This is what makes en passant unique. In every other capture in chess, the capturing piece finishes on the captured piece's square. Here it finishes behind it.
Pawns originally moved only one square at a time. The two-square first move was added to speed up the opening, which created a loophole: a pawn could use it to run straight past an enemy pawn that would otherwise have been able to challenge it.
En passant closes that loophole. It restores the position that would have arisen had the pawn advanced one square, so the two-square rule cannot be used to dodge a confrontation.
En passant is written like any other pawn capture, using the file the capturing pawn came from and the square it lands on. In the diagram above that is exd6.
The suffix e.p. is sometimes added for clarity, as in exd6 e.p. It is optional and modern notation usually leaves it out.
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