FIDE recognizes for its own tournaments and matches only one system of notation, the Algebraic System, and recommends the use of this uniform chess notation also for chess literature and periodicals. Scoresheets using a notation system other than algebraic may not be used as evidence in cases where normally the scoresheet of a player is used for that purpose. An arbiter who observes that a player is using a notation system other than the algebraic should warn the player about of this requirement. (FIDE rules)

According to the above paragraph, a player can use another system of notation, but can' not be invoked as evidence when required.

On any kind of notation system, each of the sixty-four squares is invariably indicated by a unique combination of a letter and a number.

a8	b8	c8	d8	e8	f8	g8	h8
a7	b7	c7	d7	e7	f7	g7	h7
a6	b6	c6	d6	e6	f6	g6	h6
a5	b5	c5	d5	e5	f5	g5	h5
a4	b4	c4	d4	e4	f4	g4	h4
a3	b3	c3	d3	e3	f3	g3	h3
a2	b2	c2	d2	e2	f2	g2	h2
a1	b1	c1	d1	e1	f1	g1	h1

Each move of a piece can be indicated by writing the first letter of the name of the piece, the square of departure and the square of arrival.

Every move can be described by writing the departure and arrival squares (valid and castling and pawn promotion as described below). But because this method is not economic and because if you know the piece and the arrival square then the move is determined by about 96%, so the chess notation was introduced as follows:

a) Each move of a piece is indicated by writing the first letter (P, N, B, R, Q, K) of the name of the piece (if not a pawn), and the square of arrival.

b) If two identical pieces can move to the same square, before the square of arrival it is written:
1) the rank of the square of departure, and if this can’ not make the move clear
2) the file of the square of departure, and if this can’ not make the move clear
3) the square of departure

When a pawn takes written before the arrival square the rank of the square of departure. In case of the promotion of a pawn, after the square of arrival it is written the first letter of the piece the pawn promoted to. The abbreviation for g1 castling is Ο-Ο and for c1 castling is Ο-Ο-Ο.

Example game:

1997.5.11 Computer Deep Blue - Kasparov, Garry (2785)

1 e4 c6 2 d4 d5 3 Nc3 de4 4 Ne4 Nd7 5 Ng5 Ngf6
6 Bd3 e6 7 N1f3 h6 8 Ne6 Qe7 9 O-O fe6 10 Bg6 Kd8
11 Bf4 b5 12 a4 Bb7 13 Re1 Nd5 14 Bg3 Kc8 15 ab5 cb5
16 Qd3 Bc6 17 Bf5 ef5 18 Re7 Be7 19 c4 1-0

In previous way if does not distinguish between pawns and pieces and do not write the first letter of the piece then the above game is written:

1 e4 cc6 2 d4 d5 3 bc3 e4 4 e4 bd7 5 eg5 gf6
6 fd3 e6 7 g1f3 h6 8 e6 de7 9 h1 fe6 10 g6 8d8
11 f4 b5 12 a4 b7 13 f1e1 d5 14 fg3 dc8 15 b5 b5
16 dd3 c6 17 gf5 f5 18 e7 fe7 19 cc4 1-0

In classical chess castling could be described by the departure and arrival square of the move of King but this does not always make clear this move in chess with random starting position. For this reason the castle is written as the king takes his rook who is castling. So the castle briefly written with the square of the rook who is castling.

The promotion of the pawn to a queen does not change this basic description of departure and arrival square. If you are promoting something else then write the corresponding arrival square which is not real. Fixed for reasons of symmetry (white and black pawn) and to be the chess move (ie, diagonal, straight or knight) as follows: To promote pawn to R, B, N it is respected arrival square 1, 2, 3 squares back from where is the avatar and if pawn takes then from there promoted.

The 12 possible moves that could have promoted a pawn will be written briefly as follows:

White pawn on b7:

Promoting to a8				Promoting to b8				Promoting to c8
ba8Q	ba8R	ba8B	ba8N	b8Q	b8R	b8B	b8N	bc8Q	bc8R	bc8B	bc8N
a8	a7	a6	a5	b8	b6	b5	b4	c8	c7	c6	c5

Black pawn on b2:

Promoting to a1				Promoting to b1				Promoting to c1
ba1Q	ba1R	ba1B	ba1N	b1Q	b1R	b1B	b1N	bc1Q	bc1R	bc1B	bc1N
a1	a2	a3	a4	b1	b3	b4	b5	c1	c2	c3	c4

In addition to the previous way of moves writing if the default priority order transition pieces in the arrival square is considered, not to repeat the details in each move the value of pieces P, N, B, R, Q, K, in the most common takes and generally in moves on controlled squares from the opposing faction, then the above game is written:

1 e4 c6 2 d4 d5 3 bc3 e4 4 e4 d7 5 g5 gf6
6 d3 e6 7 1f3 h6 8 e6 de7 9 h1 e6 10 g6 8d8
11 f4 b5 12 a4 b7 13 1e1 d5 14 fg3 dc8 15 b5 b5
16 dd3 c6 17 f5 f5 18 e7 fe7 19 c4 1-0

In the first 20 moves of the game the economy compared with the classical chess notation is 10% and from there can be up to 20%. In 100 random moves for these three modes the result is the following comparison table:

Characters per move	2	3	4	Average characters per move
With start symbol	20	76	4	(2*20+3*76+4*4)/100=284/100=2.84
Without start symbol	55	44	1	(2*55+3*44+1*4)/100=245/100=2.46
Without start symbol with a predetermined priority	77	23	0	(2*77+3*23+0*4)/100=213/100=2.13

The reasons for proposing a slightly different notation from the classic chess notation is that is "more international" since it not uses symbols for the pieces, the management of text for printing or for chess programs is easier, the player reads or writes earning less wining sharpness and time.