The roots of algebraic notation go back a very long way but many chess books published in the past used a different system known as descriptive notation. This was dominant until around the 1970s but all new publications now use the algebraic system.
The ranks (horizontal rows) are numbered from 1 on White’s side of the board to 8 on Black’s side of the board. The files (vertical columns) are identified by the lower case letters from "a" to "h" with the a-file on the left and the h-file on the right. This is from White’s point of view. For Black, the a-file is on the right and the h-file on the left. The squares are indicated by combining the file and rank.
From White’s point of view: a1 is in the bottom left corner of the board, a8 in the top left, h8 in the top right and h1 in the bottom right.
From Black’s point of view: a1 is in the top right corner, a8 in the bottom right, h8 in the bottom left and h1 in the top left.
Pieces are represented by a single upper case letter. K = King, Q = Queen, R =Rook, B=Bishop and N = Knight.
A move is written by writing down the piece followed by the square. For example: Nf3, Nc6, Bb5, Qd3, etc.
Pawns are not represented by any letter and pawn moves are written simply as the square the pawn moves to. EG: e4, e5, etc.
Moves are written in pairs (White’s move and Black’s reply) and preceded by the number of the move. EG: 1. e4 e5 2. Nf3 Nc6 3. Bb5 a6.
Captures are indicated by a lower case letter "x" written between the capturing piece and the square on which it lands. Pawns are indicated by writing the file of the Pawn.
EG: 1. e4 d5 2. exd5 Qxd5
En passant captures need no special notation since it is obvious from the square how the capture occured.
EG: 1 e4 d5 2. e5 f5 3. exf6.
If more than one piece of the same type can reach the same square, the piece is followed by its file and then the square it moves to. EG: Knights on b1 and f3 can both move to d2. The notation would be Nbd2 or Nfd2.
If two pieces on the same file can reach the same square, the piece is followed by its rank. EG: Rooks on c1 and c7 can both reach c4. The notation would be R1c4 or R7c4.
In very rare cases, it may be necessary to write down both the file and rank on which the piece stands before and after the move. EG: three Queens standing on b2, b8 and h2, can all reach e5. The options are Qhe5, Q8e5 and Qb2e5.
The notation for castling does not include the letters for King or Rook. Instead, the digit zero or an upper case letter “O” is written twice for King-side castling and three times for Queen-side castling. The characters are separated by hyphens. IE: 0-0 for short castling and 0-0-0 for long castling.
When a pawn is promoted, the new piece is written immediately after the square. EG: d8Q or c1N. An equals sign is often written between the square and the piece (e.g. d8=Q) and computer software will always record moves in this way. You may also sometimes see a slash written between the square and piece (e.g. d8/Q) although this is rare.
Check and Checkmate
It is not a formal requirement to indicate check or checkmate when recording a game although many players do. Books will always indicate the fact.
If a piece delivers check the move is immediately followed by a plus sign (e.g. Qd4+). For checkmate the move is followed by a hash symbol (e.g. Qf8#).
There is usually no special notation for double check (it is notated as a regular check) but it is sometimes specifically indicated by writing two plus signs (e.g. Nd6++) or even with an abbreviation such as “dbl ck”. Confusingly, some older manuscripts indicate checkmate with two plus signs.
Recording the result
The result of the game is written as 1-0 if White wins, 0-1 if Black wins, and 1/2-1/2 for a draw.
EG: 1. f4 e6 2. g4 Qh4# 0-1
Offering a draw
FIDE rules require that the offer of a draw be indicated by an equals sign in round brackets. EG: 54. Qd2 Qf6 55. Qd3 (=) Qf7 56. Qd2. The acceptance or rejection of the draw is indicated by the following notation, either the result (1/2-1/2) or the next move in the game.
There are a small number of special notations used to add simple observations about a move. A single exclamation mark shows a good move and two shows a brilliant move. A single question mark shows a bad move and two shows a blunder. An exclamation mark followed by a question mark shows an interesting move and a question mark followed by an exclamation mark shows a dubious move. The anotation is written immediately after the rank without a space (e.g. f4!?).