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Besides the Classic Chinese Mahjong, from which you can consult the Mahjong rules and the Mahjong history, there are many variations of this game. Here are the main ones:

Shanghai Mahjong : Name given to the online mahjong game which is played solo. This puzzle game is also called "Mahjong Solitaire". You will find here many free Shanghai Mahjong.

Japanese Mahjong : The Japanese mahjong game only uses 136 tiles and leaves aside the 4 seasons and 4 flowers tiles. It is certainly the most complex and subtle variation. As in China, Japanese Mahjong is often played with money and there are competitions and professionals in this game

American Mahjongg : The American variant of mahjong uses joker tiles called "the Charleston". It also differences in the scoring. Note that the spelling of mahjongg is 2g in America.

Other mahjong variations exist, particularly in the various Asian communities which have each made some modifications in the rules and scoring system.
Japanese MahjongJapanese Mahjong
Mahjongg Dark DimensionsMahjongg Dark Dimensions
Mahjongg DimensionsMahjongg Dimensions
War MahjongWar Mahjong
Mahjong FortunaMahjong Fortuna
WOW Connect 2WOW Connect 2
Mahjong SimpsonsMahjong Simpsons
Butterfly KyodaiButterfly Kyodai
Mahjong ShanghaiMahjong Shanghai
Mahjong GardensMahjong Gardens
Mahjong Dimensions DeluxeMahjong Dimensions Deluxe