The game was released on Playstation 3 and Xbox 360 on August 25, 2009 (North America), August 28, 2009 (Europe) and on the PC on September 15, 2009 (North America) and September 18, 2009 in Europe.
The game plays as a third-person action-adventure game, in which the player travels through the asylum and island chasing and battling well known enemies like Joker, Harley Quinn, Poison Ivy, Scarface, Killer Croc, and Bane.http://g4tv.com/games/ps3/53425/Batman-Arkham-Asylum/review/

Batman can use a range of gadgets like a batarang, an explosive compound sprayer, grappling gun, and a frequency scanner. Fighting ss based on a combination of stealth and melee fistfights.http://www.elecplay.com/review/17429
Batman can employ "detective mode", which enables him to see enemies through walls, detect trails, highlights interactive objects like gargoyle statues or grates.
Next to the main story, Batman is also able to solve puzzles by The Riddler, find riddle objects and find interview tapes. These unlock background stories and challenge levels which can be accessed outside the story mode.
http://blog.wired.com/games/2009/01/our-first-hand.html

The story for Arkham Asylum was written by Paul Dini, producer and writer for a number of animated series, and publisher Eidos Interactive has announced that it is based loosely on the Batman comics storyline. The game is set entirely within the confines of Arkham Asylum, a psychiatric institute for the criminally insane located on the outskirts of Gotham City. The Joker has taken over the asylum and Batman decides to move him out.

Many other familiar heroes and villains will make an appearance in the game, including The Riddler, Penguin and Commissioner Gordon.Kotaku: Eidos announce ANOTHER Batman Game (August 12, 2008) 1up.com: Eidos Announces Batman: Arkham Asylum (August 13, 2008)