- Algebraic,
- Descriptive, and
- Figurine.
Algebraic is the most popular notation, using single letters to identify the pieces and letter-number pairs to identify the squares. English algebraic notation uses the letters K/Q/R/B/N/P to identify the six pieces, the letters 'a' to 'h' to identify the files, and the numbers '1' to '8' to identify the ranks.
Nf3 means Knight moves to the square f3. Long algebraic is a little-used form of algebraic notation which adds the square from which the piece moves. Ng1-f3 means Knight moves from the square g1 to the square f3.
Figurine is similar to algebraic notation, except the pieces are represented by graphics instead of letters. Since figurine notation is not specific to any particular language, it is a universal system of publishing chess games which transcends human languages.
Descriptive is an older form of notation which was used for a long time in the English-speaking world. Although it has disappeared from modern use, it has accumulated so much literature that it is worthwhile to learn. It also has the advantage that a single type of square (for example the corner squares a1, h1, a8, h8) can be denoted by a single generic term ('R1' for the corner squares QR1, KR1, QR8, and KR8).
