Hypermodern chess is a development in the theory of chess that occurred in the teens and twenties, and was pioneered by the likes of
Aron Nimzovitch and
Richard Reti.
Parasiterex's statement that it is "based on the concept that you do not have to rush out and control the center" is deceptive and incomplete. In fact
Hypermodernism is a refinement on the understanding of the significance of the center.
What the Hypermoderns *did* discover, regarding the opening, is that it is not necessary to occupy the center with pawns in order to control it. It is possible to control it with pieces, like the king's knight that comes out in the Reti opening or black's queen's knight that comes out in the Indian openings. It is also possible to influence the center from a distance with fianchettoed bishops, and to otherwise postpone the advance of central pawns. The Hypermoderns knew, as Wilhelm Steinitz did, that the significance of control of the center varies with the openness or closeness of the position. They also knew that certain advantages could be gained by encouraging the opponent to overextend his pawn chain, and then undermining it, as is typified by the Alekhine Defense.
But Hypermodernism went beyond opening theory. Particularly in the case of Nimzovitch's theories, as expounded in My System, Hypermodernism was a new school of thought regarding position play. Nimzovitch developed such ideas as overprotection, prophylaxis, and the almost mystical faith that pieces gain strength through contact with strong *and* weak squares.