Center
The central squares of the chessboard: d4, e4, d5, e5.
There is also the extended center — a term Nimzowitsch brought into theory in 1913. Besides the squares named above, the extended center takes in the squares next to them, which together make up the c3-c6-f6-f3 square.
Nimzowitsch, Réti, Alekhine and others showed the value of the extended center in practice. Instead of occupying the center outright with pawns, another view of the center won acceptance — holding the center, or controlling it. Opening theory was enriched as a result by such openings as the Nimzo-Indian, the Grünfeld, the Alekhine Defense, and the Réti Opening. In these openings White (or Black) lets the opponent occupy the center with pawns, then builds up piece-and-pawn pressure against it and works to weaken the opponent's position there.
It is hard to overstate what the fight for the center is worth in a game of chess. Pawns or pieces placed in the center really are more active, and they cramp the opponent's forces. Full control of the center, in other words, is the key to any successful operation — or, as Alekhine aptly put it, "the center is the soul of chess."
Types of center
The way the pawns stand in the center has a large effect on the character of the play that follows. These are the pawn formations worth naming in the center.
Open center — the central squares are free of pawns. Piece play arises.
Fixed center — each side has one immobile pawn in the center, d4 for White and d5 for Black, say. Here the play often comes down to occupying the squares those pawns control with pieces.
Mobile center — one side has two pawns (on d4 and e4, say, or on d5 and e5) against the opponent's one (on e6 or d6 for Black, on d3 or e3 for White). The side with two pawns in the center has the advantage of being able to push one of them at a moment of its own choosing, depending on the plan it has in mind. The other side's defense lies in provoking one of those pawns forward, then blockading the pawn chain and occupying the weakened square with a piece.
Closed center — the pawn chains in the center have no mobility left, and the play shifts to the flanks.
Undecided pawn structure in the center — the pawn chains have not yet come into contact. This formation can turn into any of the ones above, and the character of the play will follow from which one it becomes.
When you make a plan, you take the motifs discussed under the types of center into account — with certain corrections in each particular case, of course.
A piece-and-pawn center often arises in the course of play as well: a knight, say, seizes a point in the center with a pawn behind it, and the opponent has no pawn that can attack it (a white knight on d5 with a pawn on e4 or c4, and a black pawn on e5).