Real Madrid Club de Futbol, to give it its full name, dates back to 1902 (there was an earlier club with a different name going back to 1897). When it was founded by its president Carlos Patros it was known as the Madrid Football club, but it is basically the same club and still wears the same colour (white). They didn't get the name of Real Madrid until 1920, though: 'real' in Spanish means royal, and the title was given to the team by Alfonso XIII, who was king of Spain at that time. Since then the club has also had a royal crown in its emblem.
In 1947 Real Madrid moved to the Santiago Bernabeu stadium, and this is still the ground for all their home matches. It holds many records and some commentators regard it as the world's greatest football team.
You can read a detailed history of Real Madrid here. To find out more about its foundation and early years, just click the dates on the right.