Once during the game, the King can make a special move. It's purpose is to give the King quick shelter in the corner.
Castling is the only situation where you can move two pieces at the same time. The pieces are always the King and one of the Rooks.
There are several restrictions on castling.
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The first restriction is that the King and the Rook to be moved are on their initial squares and haven't moved. The diagram shows the ideal case for both Kings and all four Rooks.
How do you know the Kings and Rooks haven't moved and then moved back to their initial squares? If you're playing a game with someone else, you have to remember. Sometimes beginning players forget -- 'You can't castle. You already moved that Rook'! 'No, I didn't'! 'Yes, you did'! 'Prove it'! -- In this diagram, you have to take our word for it.
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The second restriction is that the squares between the King and the Rook must be empty. Since the other pieces have all disappeared in the diagram, the condition for castling is met.
Other restrictions involve attacks on the King.