Vladimir Kramnik is a Russian Grandmaster born in 1975. He won the 1991 World Under 18 Championship and was the Russian national champion in 1990.
Without qualifying (he was picked by the titleholder) for the 2000 World Chess Championship against his mentor Garry Kasparov, he was able to win the title of World Champion with 8,5 to 6,5.
Defending his title against Peter Leko in 2004 and Veselin Topalov in 2006, he eventually lost it in the 2007 held super tournament. He lost the 2008 World Chess Championship against Anand with 4,5 to 6.
He is known for his very strong, solid defense.
He was the highest rated player in the world as early as 1996.
Garry Kasparov is an Russian Grandmaster born in 1963 and 12th World Champion. He learned the rules of chess when he was 5 years old. Quickly rising through the ranks he tied for first in the USSR Championship in 1981 and 1982.
Entering his first Candidates Tournament when he was 19, he beat Beliavsky, Korchnoi and Smyslov to challenge Anatoly Karpov for the World Championship.
Their first matched played under the rules first to 6 points with draws not counting was aborted after 48 games and a 5-3 lead for Karpov.
In the 1985 rematch Kasparov edged out Karpov 13-11 with a Black win in the 24th game.
In three rematches he defended his title narrowly with 12,5 to 11,5 and a 12 to 12 tie in which case he retained the title as the defending champion and another 12,5 to 11,5 in 1990.
He defended his title against Short and Anand to eventually lose it 2000 against his former pupil Vladimir Kramnik.
He is considerd one of the best Chess players of all times.
In this blitz game Kasparov makes a great sacrifice.