将棋 Shogi
Shogi is (in my humble opinion) the best of the Chaturana family. The simple addition of the rule that allows you to place captured pieces back on the board adds a whole extra level of complexity that is beautiful.
Also the ability for every piece to promote to something different at the third enemy rank is great.
The added 9th row with additional pieces also makes for a more complex game.
It also has a vast amount of literature (mostly in Japanese) detailing openings, mid-game strategy, tons of end game problems. Whole books of historical games and a huge following in Japan. There is even a whole channel dedicated to shogi and Igo.
The rules are easy enough to find online, so I haven't made a booklet for the game.
Shogi also has a huge array of historical variants such as Heian Shogi (the first version), Sho-Shogi, Chu-Shogi (which I gave its own section on the site), Dai Shogi, Tenjiku Shogi, etc...
The original Heian Shogi was essentially Makruk with an expanded board. There was no Kakugyo (角行) or Hisha (飛車).
Different from Makruk was the Gold General (金将) that was the replacement for the advisor type piece (one space diagonal).
After Heian Shogi a large variant was developed aptly called Dai Heian Shogi, or Big Hiean Shogi (大平安将棋). Well, in the Heian period obviously they weren't called that, but just plain Shogi and Dai Shogi.
Then (Kamakura)Dai Shogi was developed which added more powerful pieces.
Later Sho Shogi was introduced which added the Kakugyo and Hisha as well as an interesting piece called Suizou (酔象), translated as Drunk Elephant. This pieces moved like a Ousho(王将) but minus the space directly behind the piece. Go to the Sho-Shogi page for more info.
Sho-Shogi is the game that modern shogi developed from. It is said the Suizou was removed and probably around the same time the rule to allow pieces to be dropped back on the board was introduced.
Chu-Shogi is also a variant of notable awesomeness. I have made a separate page for it.
A few other even larger variants exist, Tenjiku Shogi, 16x16 board, being the most notable.
There are as well a number of small variants, mostly modern, but one created in the late 1700s called Tori Shogi.