The best players

The best players can be awarded specific lifetime titles by the world chess organization FIDE:
Grandmaster (shortened as GM; sometimes International Grandmaster or IGM is used) is awarded to world-class chess masters. Apart from World Champion, Grandmaster is the highest title a chess player can attain. Before FIDE will confer the title on a player, the player must have an Elo chess rating (see below) of at least 2500 at one time and three favorable results (called norms) in tournaments involving other Grandmasters, including some from countries other than the applicant's. There are other milestones a player can achieve to attain the title, such as winning the World Junior Championship.
International Master (shortened as IM). The conditions are similar to GM, but less demanding. The minimum rating for the IM title is 2400.
FIDE Master (shortened as FM). The usual way for a player to qualify for the FIDE Master title is by achieving a FIDE rating of 2300 or more.
Candidate Master (shortened as CM). Similar to FM, but with a FIDE rating of at least 2200.

All the titles are open to men and women. Separate women-only titles, such as Woman Grandmaster (WGM), are available. Beginning with Nona Gaprindashvili in 1978, a number of women have earned the GM title, and most of the top ten women in 2006 hold the unrestricted GM title.
As of August 2011, there are 1363 active grandmasters and 3153 international masters in the world. Top three countries with the largest numbers of grandmasters are Russia, Ukraine, and Germany, with 208, 78, and 76. The country with most grandmasters per capita is Iceland, with 11 GMs and 13 IMs among the population of 310,000.
International titles are awarded to composers and solvers of chess problems and to correspondence chess players (by the International Correspondence Chess Federation). National chess organizations may also award titles, usually to the advanced players still under the level needed for international titles; an example is the Chess expert title used in the United States.

In order to rank players, FIDE, ICCF, and national chess organizations use the Elo rating system developed by Arpad Elo. Elo is a statistical system based on the assumption that the chess performance of each player in their games is a random variable. Arpad Elo thought of a player's true skill as the average of that player's performance random variable, and showed how to estimate the average from results of player's games. The US Chess Federation implemented Elo's suggestions in 1960, and the system quickly gained recognition as being both fairer and more accurate than older systems; it was adopted by FIDE in 1970.[note 6] The highest ever FIDE rating was 2851, which Garry Kasparov had on the July 1999 and January 2000 lists.