
The Knight, always moves in an L-shaped pattern by 3 squares and can jump over other pieces (presumably due to being on horseback). Always lands on a different-coloured square to the one it moved from.

A pawn, normally moves only one square straight forward, however on its initial move can move 2 squares straight forward. If there is an opposing piece diagonally 1 square in front a pawn can capture it, however it cannot capture a piece directly in front, nor move diagonally if no piece is available to capture.
A special move called en passant is sometimes available for pawns. This is possible if a pawn makes an initial move of 2 squares but could have been captured by an opposing pawn if it had only moved 1 square. The opposing pawn is actually able to ignore the fact its enemy moved 2 squares and capture diagonally as if it had only moved 1 square, albeit only if the opposing pawn acts immediately. This is called en passant (in passing).

A pawn that reaches the opposite end of the board (the 8th rank for white, or 1st rank for black) can (and must) be promoted to another piece, usually a Queen (but not a King). This is usually highly advantageous for the promoting player.