Algebraic chess notation is the method used today by all competition chess organizations and most books, magazines, and newspapers to record and describe the play of chess games. It replaced descriptive chess notation, although the older notation can still be found in older literature.
The notation begins by identifying each square of the chessboard with a unique coordinate. First, the files (that is, lines running parallel to the direction the players are facing) are labelled with lowercase letters a through h, from the left of the "white" player. So the "a" file is to white's left, and to black's right. Then the ranks (lines running horizontally between the players) are numbered from 1 to 8, starting from white's home rank. Thus, black's home rank is rank 8. Each square of the board, then, is uniquely identified by its file letter and rank number. The white king, for example, starts the game on square e1. The black knight on b8 can move to a6 or c6 (or d7, if that square is vacant).
Each type of piece (other than pawns) is identified by an uppercase letter, usually the first letter in the name of that piece in whatever language is spoken by the player recording. English-speaking players use K for king, Q for queen, R for rook, B for bishop, and N for knight (since K is already used). Players may use different initials in other languages. For example, French players use F for bishop (from fou). Pawns are not indicated by a letter, but by the absence of such a letter.
Each move of a piece is indicated by the piece's initial, plus the coordinate of the destination square. For example Be5 (move a bishop to e5), Nf3 (move a knight to f3), c5 (move a pawn to c5--no initial in the case of pawn moves). In some publications, the pieces are indicated by graphical representations rather than by initials: for example, ♞c6 (your web browser may not be able to display that properly).
When a piece makes a capture, an x is inserted between the initial and the destination square. For example, Bxe5 (bishop captures the piece on e5). When a pawn makes a capture, the file from which the pawn departed is used in place of a piece initial. For example, exd5 (pawn on the e-file captures the piece on d5). The : after the move (Be5:) is also used for captures. En passant captures (see pawn) are specified by the capturing pawn's file of departure, the x, and the square to which it moves (not the location of the captured pawn), optionally followed by the notation "e.p."
If two identical pieces can move to the same square, the piece's initial is followed by: (1) if both pieces are on the same rank, the file of departure; (2) if both pieces are on the same file, the rank of departure. If pieces are on different ranks and files, method (1) is preferred. For example, with two knights on g1 and d2, either of which might move to f3, the move is indicated as Ngf3 or Ndf3, as appropriate. With two knights on g5 and g1, the moves are N5f3 or N1f3. As above, an x may be used to indicate a capture: for example, N5xf3. It may be necessary to identify a departing piece with both its file and its rank in unusual configurations (e.g. the player has 3 queens or 3 knights on the board). It is never necessary to specify that a capture was en passant because a capture from the same file but not en passant would have a different destination square.
If a pawn moves to its last rank, achieving promotion, the piece chosen is indicated after the move, for example e1Q, b8N. Sometimes an "=" sign is used: f8=Q.
Castling is indicated by the special notations O-O (for kingside castling) and O-O-O (queenside). Optionally, it may be indicated by the king's move; for example, Kg1.
Additional marks can be added after the move to provide more information. The mark "!" means good move, "?" means a bad move, "??" means a blunder, "?!" refers to a dubious move, while "!?" is an interesting move. "!!" is reserved for really great moves.
A move which places the opponent's king in check (see king) may have the notation "+" added. Checkmate can likewise be indicated "#" (some use "++" instead, but the U.S. Chess Federation recommends "#").
Chess games are often stored in computer files using Portable Game Notation (PGN), which uses algebraic chess notation as well as additional markings to describe a game.
Some computer programs (and people) use a variant of algebraic chess notation, termed long algebraic notation or full algebraic notation. In full algebraic notation, moves are simply written as the beginning position, a dash ("-"), and the ending position. An example would be "e2-e4". This notation takes more space and thus is not as commonly used.
The following short-hand notations are frequently used to comment moves:
= the two sides are equal in this position
+/= white is slightly better
=/+ black is slightly better
+/- white has a clear advantage
-/+ black has a clear advantage
1-0 white won
0-1 black won
! a good move
!! an excellent move
? a mistake
?? a blunder
!? an interesting move that may not be best
?! a dubious move, but not easily refuted