The notation of a game of chess
There are tens of thousands of books about chess and since the 19^{th} century numerous journals which report of chess tournaments or publish annotated games. So an easily internationally understandable form of recording chess moves is required The way of recording a chess game in writing is referred to as the notation. In tournament chess the players are both required to write down the moves of their game on socalled scoresheets.
To note down chess games we use the coordinates of the chess board
Each square is called after its file and rank. The files go from 'a' to 'h', the ranks from '1' to '8'.
The simplest way to note down a game is called long notation. It works as follows:

 Pawn moves are simply recorded by giving the starting and finishing squares, e.g. 1. d2d4
 The pairs of moves are numbered in sequence and in front of each pair there is the move number, e.g. 2. c2c4 e7e6.
 For the sake of clarity moves with pieces other than pawns start with a letter signifying which piece is moving, e.g. 3. Nb1c3 Bf8e7. These abbreviations are K, Q, R, B, N.
 Instead of a hyphen captures ar denoted by an "x", e.g. 8. Bg5xf6
 Optionally checks can be recorded with a plus sign, e.g. 3. Bf1b5+
 For a mating move the hash sign is used, e.g. 23. Bd6e7#
 Short or kingside castling is 7. 00, long or queenside castling 9. 000
 For promotions the abbreviation for the piece chosen is placed at the end of the move, e.g. 38. e7xf8Q+
 The result is abbreviated as follows. White wins: 10, Draw: 1/21/2, Black wins: 01
In today’s chess books. magazines and on the Internet one almost exclusively finds the more compact short notation. In it the starting square is left out because it is obvious. So, 1.e4 instead of 1. e2e4 and 8.Bxf6 in place of 8. Bg5xf6. If two pieces of the same type can reach the target square, a letter is added for a file from which the designated one comes or a number for a rank, in order to clear up the ambiguity. Example 6.Nbd2, if two knights can move to the d2square and you mean the knight from the bfile. Or 12.R3d4, if there are two rooks in the dfile which can both go to d4 and the rook on the third rank is the one intended to go there.
Example of the notation of a game of chess on a scoresheet: