Opening theory (chess)
Chess openings are a vital part of chess strategy. There are several purposes to the moves that a player chooses to make in the opening. Firstly, the player will attempt to control the center of the board, either by occupying it with pawns, as in classical opening theory, or by controlling it from the sides, as in hypermodern chess opening theory. Secondly, the player will attempt to get space for his pieces to operate in, particularly the bishops, which cannot move until a pawn is moved. In classical opening theory, a player will attempt to have pawns on both center squares (e4,d4), which will allow the player to move both bishops. In hypermodern opening theory, a player will usually place a pawn on c4, and fianchetto his bishops to the side, by moving the g and b pawns one square, and moving the bishops to g2 and b2. Thirdly, a player will frequently try to move certain pieces off the back rank of squares so that the king and a rook can perform the castling maneuver, putting the king in a less vulnerable position, early in the game.
King pawn openings
Chess openings are usually classified by the first move that white makes. King pawn openings are all openings that begin with (1.e4). The classical defense to the king pawn opening is (1.e4 e5), where black attempts to counter white's occupation of the center, and develop his own kingside bishop. Popular variations on this include the Ruy Lopez, or Spanish game (1.e4 e5 2. Nf3 Nc6 3. Bb5), The Giuoco Piano, or Italian game (1. e4 e5 2. Nf3 Nc6 Bc4 Bc5), and the Petroff Defense (1. e4 e5 2.Nf3 Nf6).
Other, less common defenses to (1.e4) include the French defense (1. e4 e6), with the intention of pushing to d pawn to d5, supported by the pawn at e6. There is also the Pirc defense (1.e4 d6) where black typically fianchettoes the kingside bishop, and later uses the pawn break e5 or c5. Alexander Alekhine pioneered the move (1.e4 Nf6), in which white attacks black's knight, and attempts to occupy the center of the board, while black attempts to counterattack and crack white's control of the middle.
Today, the most common defense in King Pawn games is the Sicilian (1.e4 c5). It relies somewhat on hypermodern principles of controlling the center from the sides, but also leaves both of black's center pawns in place, to attempt a counterattack in the center later in the game.
Queen pawn openings
Queen pawn openings begin with white playing (1.d4). When black responds with (1...d5), white's most common response is the Queen's Gambit (2 c4). Black can accept the gambit (2... dxc4), or more commonly play the Queen Gambit Declined (2...e6) where black's position is slightly cramped by the inability of his bishop to move, or the Slav Defense (2....c6), where black threatens to win the c pawn.
Instead of pushing the d pawn, black can play other moves. (1d4 Nf6 2. c4 g6) is the most common response today, known as the King's Indian Defense. Black will fianchetto the bishop, and attempt a counterattack in the center later in the game. Alternatively, Black can play the Queen's Indian Defense with (1 d4 Nf6 2. C4 e6 3. Nf3 b6).
Other opening moves
There are several hypermodern systems, that often transpose, but generally center around the same group of opening moves. White can play the English opening (1. c4), the Reti (1. Nf3 d5 2. c4) or the Barcza (1. Nf3 d5 g3). All of these systems tend to center around a white fianchetto of the kingside bishop, a kingside castle, allowing black to set up in the center and attempting a counterattack.
Interestingly, hypermodern openings are often used by grandmasters when playing against opponents of much lower skill level, because these opening systems tend to be considered less "sharp", that is a small error in the opening is far less likely to cost a player the game. Also, grandmasters may not wish to reveal any innovative position they may have discovered through study, in an opening that is used at grandmaster level.
Obviously white can play dozens of other opening moves, but very few of these are used at advanced stages of play.