The Madrid Airport is called Madrid Barajas Airport and is located 12 km from center of Madrid. It is the first Spanish airport by passenger traffic and operations.

Barajas Airport has 4 terminals (T1, T2, T3 and T4). T4 is the most recent and is separated 2 kmfrom other terminals. A free shuttle service (airport shuttle) connects all Terminals
 
Official website Madrid-Barajas Airport

The Madrid-Barajas Airport is connected to Madrid by:

Metro.Line 8

City Bus. The line 101 and line 200 connects the T1, T2 and T3 with the center of Madrid. The line 204 connects T4 with the center of Madrid

Intercity buses. line 822, line 824, line 827, line 828, line 211, line 212, line 214, line 256 and line 263.

Taxi. At the exit of each of the terminals there is a taxi stop. Taxi Fares Information