Italian opening is one of the oldest chess openings. It was analyzed by the greatest Italian masters in XVI century. The main idea for white is formation of ideal pawn center by playing c2-c3 and pushing d2-d4.
Black has a weak f7 square, which white using as a target for its attacks. However, black found very effective way to fight against these threats.

1. e4 e5 2. Nf3 Nc6 3. Bc4

The main variations are:

3…Bc5
Until the 19th century the main line of the Italian Game. Dubbed the Giuoco Piano ("Quiet Game") in contra-distinction to the more aggressive lines then being developed, this continues 4.d3, the positional Giuoco Pianissimo ("Very Quiet Game"), or the main line 4.c3 (the original Giuoco Piano) leading to positions first analyzed by Greco in the 17th Century, and re-vitalized at the turn of the 20th by the Moller Attack.
This variation also contains the aggressive Evans Gambit (4.b4), and the Jerome Gambit (4.Bxf7+), both 19th Century attempts to open up the game.
3…Nf6
Leading to the more aggressive Two Knights Defense; again, this is more in the nature of a counter-attack, and some (eg Chigorin) have proposed it be re-named so. The Two Knights Defence contains the knife-edged Traxler/Wilkes-Barre Variation, the aggressive Fegatello (or Fried Liver) Attack, and the complex Max Lange Attack.
3…Be7
Leading to the Hungarian Defence, a solid, drawish game which is often chosen in tournament play to avoid the complexities and risks of the other lines.
3…d6
The Paris Defence, another solid positional line; this was popular in the late 19th and early 20th centuries, but hardly seen now.