This Hexagonal Chess Collection includes McCooey's Hexagonal Chess, Glinski's hexagonal chess, mini-Hex chess by Dave McCooey, and Grand Hexachess by Derick Peterson.
 
Basically, HexChess is a game of chess played on a base-6 hexagonal board. All rules are adapted to the new board shape as closely as possible.
The major change from a square-shaped to a hex-shaped board involves the number of squares which are considered adjacent to another square. On the normal chess board, a square usually has 8 neighbours. On the hex-board, a square (or better, a hex) has 12 neigbours: There are now 6 'orthogonal' and 6 'diagonal' directions, as opposed to 4 each.
Consequently, 3 different colours are used to make orientation easier, so when moving in an 'orthogonal' direction, the hex colour changes with every step. When moving 'diagonally', it stays the same. A side effect of this point of view is that 'diagonally' moving pieces appear to 'jump' hexes, which is not really true: The Knight remains the only jumping piece.
 
This hex-transition by Dave McCooey is one of the more logical ones. Most chess rules remained, and everything works as one would expect it. The rule changes in detail:
1. There is no castling.
2. The centre Pawn may not double-step.
(The second change was made in order to disallow White to seize the centre with her first move.)
 
Due to the increased mobility of pieces, the material that can force checkmate in the endgame has also changed. Among other observations, Mr McCooey found out that two Knights can now force checkmate against the lone King. You may try this for a challenge.