Chess notation is a way to record and communicate chess moves. Nearly all chess players record all the moves (his and his opponent) of their serious games. There are two major methods of chess notation. The first method is the descriptive notation and the second method is the algebraic notation.
The descriptive notation has been around the longest and is the method found in older chess books and magazines.
The descriptive method names the files according to the piece in the initial postion. So, reading from left to right, the first file is the Queen Rook (QR) file, the next file is the Queen Knight (QN) file, then the Queen Bishop (QB) file, then the Queen (Q) file, then the King (K) file, then the King Bishop (KB) file, then the King Knight (KN) file, then the King Rook (KR) file.
The pawn is represented by a P. The knight is represented by a N (or Kt, but not K because that is the king). The bishop is represented by a B. The rook is represented by an R. The queen is represented by a Q. The king is represented by a K.
From bottom rank to the top rank, each rank counts up from 1 to 2 to 3 to 4 to 5 to 6 to 7 to the 8th rank.
The chess squares have different notations, depending upon the White point of view or the Black point of view.
The square in the lower left is QR1 (Queen Rook 1) for White or QR8 (Queen Rook 8) for Black. The square in the upper right is KR8 for White and KR1 for Black.
The chess board is always set up for the light colored square (usually White) to the right and the placement of the Queen on its own color. So the White Queen is on the White square (Q1 for White or Q8 for Black) and the Black Queen is on the Black square (Q8 for White or Q1 for Black).
Castling on the King side is noted O-O. Castling on the Queen side in O-O-O.
Promoting a pawn to a queen would be something like P-QR8=Q.
When there are two possible moves, you distinguish the right move by indicating if it is on the kingside or queenside. So the Knight to Bishop 3 could be two choices. It could be N-QB3 or N-KB3 depending if it is on the queen side or king side.
A capture is indicated by an x. So, if Bishop takes Knight, it is BxN.
A check is optional in notation, but it could be indicated with a plus symbol (+) or by the check symbol (ch). Checkmate may use the '++' (some books use this symbol for double check) symbol or the '#' symbol.
Taking a pawn en passant is usually written PxP e.p.
A bad move has a question mark (?). A very bad move has two question marks (??). A good move may be marked with a ! after it. A very good move may be marked with two !! after it. An interesting move is indicated with a !? and a dubious move is indicated with a ?! after the move.
If White won, then it will end with 1-0. If Black won, it will end with 0-1. If it is a draw, it may end with a 1/2-1/2 symbol.
The best way to learn is by example. Here is a short game in descriptive notation. The opening is the King's Gambit Accepted.
1.P-K4 P-K4 2.P-KB4 PxP 3.N-KB3 B-K2 4.B-B4 B-R5+ 5.NxB QxN+ 6.P-KN3 PxP 7.O-O QxP mate 0-1 Carta-Cassano, Italy 1980
The same game in algebraic notation is:
1.e4 e5 2.f4 exf4 3.Nf3 Be7 4.Bc4 Bh4+ 5.Nxh4 Qxh4+ 6.g3 fxg3 7.O-O Qxh2 # 0-1 Carta-Cassano, Italy 1980.
Here is another example.
1.P-K4 P-K4 2.P-KB4 PxP 3.N-KB3 Q-K2 4.P-Q4 QxPch 5.B-K2 B-N5ch 6.P-B3 B-R4 7.O-O P-Q3 8.B-N5ch K-B1 9.R-K1 Q-Q4 10.R-K8 mate 1-0 Wall-Atnas, Internet 2003
In algebraic, it is:
1.e4 e5 2.f4 exf4 3.Nf3 Qe7 4.d4 Qxe4+ 5.Be2 Bb4+ 6.c3 Ba5 7.O-O d6 8.Bb5+ Kf8 9.Re1 Qd5 10.Re8 mate 1-0 Wall Atnas, Internet 2003
The algebraic notation is now the most common notation and a standard in all major chess tournaments. It is called algebraic because of the unique way it identifies each chess square on an 8 by 8 matrix chess board. Each column (file) is labeled with a letter. Each row (rank) is labeled with a number. Some chess boards have these letters and numbers written on the sides (letters) and top and bottom (numbers).
In algebraic notation, the columns, from left to right, are a, b, c, d, e, f, g, h starting from the White side. The rows are numbered 1, 2, 3, 4, 5, 6, 7, 8 from the White point of view. So, from left to right, we have a1, b1, c1, d1, e1, f1, g1, h1. The sqaure in the lower left is a1 and the square in the upper right is h8. The board is usually displayed with the White at the bottom and the Black at the top.
The main thing to remember when looking at a chess diagram, is that the board is always "right side up" for White, meaning White is always shown as playing from the "bottom" of the board. The board is always "upside down" for Black. And in algebraic notation, Black must think in reverse. From Black's point of view, the letters from left to right are h, g, f, e, d, c, b, a and the rows start at 8 and go from bottom to top as 8, 7, 6, 5, 4, 3, 2, 1.
The pieces are identified as follows: N for Knight, B for Bishop, R for Rook, Q for Queen, and K for King. The pawn may be given a P, but it is understood that it is a pawn if there is no letter in front of it. The pieces are capitalized and the squares it moves to are in lower case (Bb5 is Bishop to the b5 square).
A move is a combination of the moving piece plus the square to which it is moving. The move Nf3 means the Knight moved to the f3 square. A move e4 means the Pawn moved to the e4 square.
Castling on the kingside is O-O. Castling on the queenside is O-O-O.
Promoting a pawn to a queen would be something like a8=Q, meaning a White Queen Rook Pawn made it to the 8th rank and is being promoted to a Queen. It could have been promoted to a Knight, Bishop, or Rook, but you generally want the most powerful piece.
An ambiguous move is made clearer by inserting the file of the moving piece immediately after the letter denoting the piece. For example, if I had the original White Knight on g1 (Ng1) and my other White Knight was on d4 (Nd4), instead of writing Nf3 (either knight could do that), I would write Ngf3 if it were the Knight on g1 or Ndf3 if it were the Knight on d4.
A capture is sometimes denoted with an 'x'. PxP could be exf4. NxB could be Nxh4 (or just Nh4).
A check is indicated optionally by a '+'.
Sometimes moves have a space after the period (1. e4), and sometimes ther is no space after the period (1.e4).
Here is the same game from the descriptive notation section in algebraic method again:
1.e4 e5 2.f4 exf4 3.Nf3 Be7 4.Bc4 Bh4+ 5.Nxh4 Qxh4+ 6.g3 fxg3 7.O-O Qxh2 mate 0-1 Carta-Cassano, Italy 1980.
Or, 1.e4 e5 2.f4 ef4 3.Nf3 Be7 4.Bc4 Bh4 5.Nh4 Qh4 6.g3 fg3 7.O-O Qh2# 0-1
Databases may be in Portable Game Notation (PGN). It is a standard header for text files. It uses algebraic with headers. It may look like this.
[Event "World Ch Match"]
[Site "Reykjavik, Iceland"]
[White "Spassky, Boris"]
[Black "Fischer, Robert"]
1.d4 Nf6 2.c4 e6 3.Nc3 Bb4 4.Nf3 c5 5.e3 Nc6 6.Bd3 Bxc3 7.bxc3 d6 8.e4 e5 9.d5 Ne7 10.Nh4 h6 11.f4 Ng6 12.Nxg6 fxg6 13.fxe5 dxe5 14.Be3 b6 15.O-O O-O 16.a4 a5 17.Rb1 Bd7 18.Rb2 Rb8 19.Rbf2 Qe7 20.Bc2 g5 21.Bd2 Qe8 22.Be1 Qg6 23.Qd3 Nh5 24.Rxf8 Rxf8 25.Rxf8 Kxf8 26.Bd1 Nf4 27.Qc2 Bxa4 0-1