I propose here a notation for recording games. It is based heavily on chess notation, and was developed for use in the applet on this site.
As the board has rotational symmetry, those recording a game must decide from what direction they will view the board. Once done, the files are lettered starting with A on the left, not omitting letters I nor O for games that are large enough. Upper or lower case letters may be used at discretion. The ranks are numbered from 1 at the bottom.
A normal non-capturing move is represented as in chess co-ordinate notation, using the hyphen between the origin and destination squares, as in: E5-E8. For brevity, capturing moves may use this notation, but for clarity it is suggested that captures are explicitly stated as follows.
As a capture will occur on a square beside the destination, rather than the destination square as in chess, the captured piece must be identified explicitly. This is done by appending "x" and the square co-ordinates after the move, for instance, E5-E8xF8.
A move in hnefatafl can capture up to three pieces. If two or more pieces are captured in a move, the squares of the captured pieces are separated by a slash "/" character, as in E5-E8xD8/F8/E9.
If a move by the defending side gives the king a path to victory, a "+" may be appended to the move. Similarly, if a move by the attackers threatens the king with capture, a "+" may be added. These are analogous to "check" in chess. Note that the applet on this site does not support this part of the notation.
A winning move, that is, the escape or capture of the king, should have a "++" suffix.
If a player makes a suicidal move that would immediately end the game, this should be suffixed with "--". This may happen in a game between beginners if, neither having noticed that the king has one route to his exit, the attacker then opens up a second route; in this example the king would automatically have won without having to make a further move.
The "--" on its own could be used to signify a resignation.