Algebraic notation is the standard method for recording and describing the moves in a game of chess. It is based on a system of coordinates to uniquely identify each square on the chessboard.
Naming the squares
Each square of the chessboard is identified by a unique coordinate pair—a letter and a number—from White's point of view. The vertical columns of squares, called files, are labeled a through h from White's left (the queenside) to right (the kingside). The horizontal rows of squares, called ranks, are numbered 1 to 8 starting from White's side of the board. Thus each square has a unique identification of file letter followed by rank number. For example, the initial square of White's king is designated as "e1".
Naming the pieces
Each piece type (other than pawns) is identified by an uppercase letter. English-speaking players use the following letters:
K = King
Q = Queen
R = Rook
B = Bishop
N = kNight
Pawns are not identified by an uppercase letter, but rather by the absence of one. Distinguishing between pawns is not done when recording moves (pawn captures are an exception and indicated differently as explained below), since only one pawn can move to a given square.
x = capture
+ = check
++ = doublecheck
# = checkmate
O-O = castles short on the king's side
O-O-O = castles long on the queen's side
e.p. = en passant
Notation for moves
Each move of a piece is indicated by the piece's uppercase letter, plus the coordinate of the destination square. For example, Be5 (move a bishop to e5), Nf3 (move a knight to f3). For pawn moves, a letter indicating pawn is not used, only the destination square is given. For example, c5 (move a pawn to c5).
This is what a game would look like on the chessboard:
1. f4 e5
2. fxe5 d6
3. exd6 Bxd6
4. g3 Qg5
5. Nf3 Qxg3+
6. hxg3 Bxg3#
This is what this game would look like using algebraic notation:
1. f4 e5 The White pawn moves to f4 and the Black pawn to e5.
2. fxe5 d6 The White pawn on the f file takes the pawn on e5. The Black pawn moves to d6.
3. exd6 Bxd6 The White pawn on the e file takes the pawn on d6. The Black Bishop takes the pawn on d6.
4. g3 Qg5 The White pawn moves to g3. The Black Queen moves to g5.
5. Nf3 Qxg3+ The White Knight moves to f3. The Black Queen takes the pawn on g3 and checks the White King.
6. hxg3 Bxg3# The White pawn on the h file takes the Queen on g3. The Black Bishop takes the pawn on g3 and delivers checkmate.