A couple of additions and a correction. First, he is from Baku (Now called Baki), Azerbaijan. He currently resides in Moscow.
He is widely known for his aggressive play, and his uncanny ability to absorb information. He uses a full team of top players and vast computing resources to prepare for his opponents. It has often been speculated whether Bobby Fischer in his prime could have beaten Kasparov in his. Fischer went insane and is well past his prime, so it's pretty difficult to say. Kasparov is arguably the strongest player who has ever lived.
Kasparov was raised as a chess prodigy, and tutored by Mikhail Botvinnik, a former World Champion. Kasparov himself became World Champion at the age of 22. He has been known to be very emotional and has often been accused of poor sportsmanship. A case in point is when he lost to IBM's Deep Blue. He complained about a number of aspects of the game and even accused the operator of the computer of cheating. Kasparov was subsequently lambasted by the press.
Even though he lost the BrainGames World Championship match in November 2000, he is still considered the strongest player in the world by FIDE ratings. He also recently proved himself to be back in shape by nailing down the Wijk Aan Zee 2001 Super-GM tournament in January with a solid 9 points. Interestingly, he faced the new World Champion, Vladimir Kramnik for the first time since the title match in this event, and threw away a solid game on move 40 to end with a draw.
There are a couple of biographies available. One is Mortal Games by Fred Waitzkin (Author of Searching For Bobby Fischer) and the other is an autobiography titled Unlimited Challenge. He is also the author of numerous chess books and articles, and is currently very devoted to building his web presence, KasparovChess.com.