This has been the most popular variation of the Sicilian Defense in chess ever since Bobby Fischer used it as the mainstay of his opening repertoire with Black and put together a string of stunning victories. Devised by Grandmaster Miguel Najdorf (pronounced 'Ny-dorf'), the Najdorf variation has accumulated a truly enormous body of theoretical analysis and tournament practice, including some of the most complicated and unclear games of chess that it is possible to play.

The beginning moves are:

1.e4 c5
2.Nf3 d6
3.d4 cxd4
4.Nxd4 Nf6
5.Nc3 a6

+----+----+----+----+----+----+----+----+
| r  | n  | b  | q  | k  | b  |    | r  |
+----+----+----+----+----+----+----+----+ 
|    | p  |    |    | p  | p  | p  | p  |
+----+----+----+----+----+----+----+----+
| p  |    |    | p  |    | n  |    |    | 
+----+----+----+----+----+----+----+----+
|    |    |    |    |    |    |    |    | 
+----+----+----+----+----+----+----+----+
|    |    |    | N  | P  |    |    |    | 
+----+----+----+----+----+----+----+----+
|    |    | N  |    |    |    |    |    | 
+----+----+----+----+----+----+----+----+
| P  | P  | P  |    |    | P  | P  | P  | 
+----+----+----+----+----+----+----+----+ 
| R  |    | B  | Q  | K  | B  |    | R  |
+----+----+----+----+----+----+----+----+

The idea of the pawn move to a6 is not immediately obvious. Basically, Black is going to try and defuse White's lead in development by grabbing a share of the center of the board with the pawn push e7-e5. However, to play this immediately can result in disaster:

5...e5?
6.Bb5+ Bd7
7.Nf5!

Black is now in serious trouble. Therefore, it is necessary to prepare for the e7-e5 advance by playing a6, which will prevent the White bishop from giving check on b5. Also, it prepares for the later advance b7-b5, claiming space on the queenside.

White has several options against the Najdorf variation, which split up roughly into two main types: those which allow Black to play e7-e5, and those which prevent it. Of the former, the main line can continue:

6.Be2 e5
7.Nb3 Be7
8.o-o Be6

In this position, Black is not so vulnerable to a kingside attack, but can have long-term problems resulting from his 'backward' pawn on d6, which can only be defended by pieces. The alternative main line for White, and the one which has spawned most of the huge amount of theory on the Najdorf, is as follows:

6.Bg5 e6
White's last move prevents e7-e5 due to the nasty reply 7.Bxf6! which will either give White a devastating initiative, or destroy Black's pawn structure for good.
7.f4 Be7

The theoretical analysis must stop here, as there are already multiple important possibilities for Black on the last move, including 7...Qb6, the Poisoned Pawn variation, which is incredibly complex and unclear, with published theoretical variations going as deep as 30 moves in some lines. However, the main ideas are clear: White will attack all-out in the center and the kingside, and Black will try to rely on the inherent solidity of his position, and time his counter-attack properly on the queenside (or the center).

Even after decades of exhaustive study, the Najdorf retains its attraction for the world's top players, and new ideas constantly appear in tournaments and periodicals. Just like its sister variation, the Dragon, it is an excellent way for Black to try and unbalance the position and create complications right from the beginning - however, it requires deep theoretical knowledge and a lot of study, and therefore is not ideal for players who don't want to keep up with all the latest trends and analysis.