Who is the best chess player ever? What is the best game ever played? These are hard questions to answer, and nobody really knows the truth, because it is a matter of opinion. But for many people the answers to those questions are 1. Garry Kasparov, and 2. Kasparov-Topalov from Wijk ann Zee, 1999.
Garry Kasparov was born in the city of Baku. He was the youngest ever world champion (he became the champion of the world at 22 years old!) after he beat Anatoly Karpov in a match in 1985. He stayed world champion until he lost in an upset to Vladimir Kramnik in 2000. He was almost always the highest rated player in the world.
Kasparov played in his first international tournament by mistake! His country sent him to a tournament in the city of Banja Luka when he didn't even have a rating. They thought it was a junior tournament (for kids). It wasn't - actually, it was a grandmaster tournament. This didn't bother Kasparov, though. He won it and got a first rating that was #15 in the world!
His game against Veselin Topalov from Bulgaria (who wasn't a bad player himself and later also became World Champion) is considered by many to be the best game ever. Kasparov sacrificed two rooks and drove the black king to a strange little cubby-hole on the side of the board where it faced the danger of being checkmated in different ways. Then the king escaped to run down toward White's king, where finally a fierce cross-pin finished it off.
The game is very complicated so just enjoy watching such an amazing adventure!
The first part of the game has been a fairly quiet maneuvering battle. It looks like Topalov has done very well. He is trying to trade queens. White's pawn on d5 looks like it will not survive long, and the knight on a5 could be very bad for White if the queens are traded.
But while Topalov was breaking through in the center, Kasparov was not just wasting time. His pieces don't look very coordinated but just see what happens! The black king is open and Kasparov has some surprises planned.