The king can move one square in any direction. In chess if your king is under attack that is called "Check" and you are forced to make a move that gets your king out of check. If there are no moves available that let your king escape check, then that is called "Checkmate" which means you lose. Your goal is to checkmate the opponents king while defending your own.
The queen can move diagonally, horizontally, and vertically. The queen is the most powerful piece of them all. The queen is the most common piece used to deliver checkmates since you only need her and another piece to defend her to checkmate a king.
The rook can move horizontally and vertically. There is also a special move called castling where the king moves two squares to either side, with the rook moving to the other side of the king. Castling is not possible if either the king or rook has moved, or if the king would move into, out of, or through a check. Castling allows you to get your king to safety in the corner while also bringing out a rook, getting it into action and connecting it with your other rook which is good because rooks work well when supporting each other.
The bishop moves diagonally. Because the bishop can only move diagonally this means it can't move to different colored squares and will always stay on the color it started on. The light-squared bishop would only stay on light squares, and the dark-squared bishop would only stay on dark squares.
The knight moves in a L shape, two squares vertically and one square horizontally, or two squares horizontally and one square vertically. The knight has the special ability of being able to jump over pieces
Generally the pawn can only move one square at a time, one square vertically but captures are one diagonally. The exception to this is if it is the pawn's first move, in this case the pawn can move two squares forward instead of one.
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