Betza's funny notation ones. The notation is based on dividing moves that can be made on a board of squares into groups of symmetry-equivalent moves, the moves within a group differing only in the direction in which the step is taken. Each such group (referred to as "atom") is indicated by a capital, such as N for the 8 moves of the knight. The letter that represents the atom is usually the first letter of the simplest piece from current or historic chess variants that has this move, such as A and F for the alfil and ferz of shatranj (ancient Arabic/Persian chess).
Fairy chess piece here for "initial" in the description of the different types of pawns. The letter a is used here to describe again, indicating the piece can make the move on which it is prefixed multiple times, possibly with new modifiers mentioned behind the a, which then apply to the second 'leg' of the move. Directional specifications for such a continuation step should be interpreted relative to the first step (e.g. aW is a two-step orthogonal move that can change direction; afW is a two-step orthogonal move that must continue the same direction). To handle some frequently encountered special moves, e can