This is one of the earliest 3D Chess games for the 8x8x8 playing field. Each player's force consists of 64 pieces arrayed on the four central levels.
 

Archbishop [A]	slides diagonal or triagonal.
Bishop [B]	slides diagonal.
Favourite [Fa]	slides diagonal or orthogonal.
Fool [Fo]	slides triagonal.
Hippogriff [H]	leaps to the opposite corner of a 2x3x4 area.
King [K]	steps orthogonal, diagonal or triagonal.
Pawn [P]	steps one vacant forward orthogonal or two on the first move, captures one forward diagonal or triagonal.
Queen [Q]	slides orthogonal, diagonal or triagonal.
Rook [R]	slides orthogonal.
Space Knight [N]	leaps to the opposite corner of a 1x2x3, 2x2x3 or 2x3x3 area.

A castling move may be preformed by the King on its initial level, with the usual restrictions.
Pawns may also perform en passant captures. Remember that such can occur in 3D.
 
The game is won by checkmating the opponent King.