How to reach...

... the Universidad Autónoma de Madrid from the Adolfo Suárez-Madrid-Barajas Airport

By bus: is the easiest, quickest and cheapest way. The trip takes around 25 minutes. Intercity Bus Route 827 and 828 runs from terminal T4 of the airport to UAM (towards Canillejas-Alcobendas-Tres Cantos or Canillejas-Alcobendas-Universidad Autónoma). Here you can find the location of the bus stop at the terminal T4. The fare is 2,00 EUR / one-way ticket. It runs from 6:30 to 23:10 approximately. There are free shuttle buses connecting terminals T1-T2-T3 and T4.

By train: The trip takes around 35 minutes in Cercanías (local train). Take Cercanías line C-1 from Terminal T4 towards Príncipe Pío station (here you can find the location of the Cercanías station at the Terminal T4) and get off in Chamartín station. Change to Cercanías line C-4 towards Alcobendas/San Sebastián de los Reyes or Colmenar Viejo. The destination is "Cantoblanco Universidad". The fare is 2,60 EUR / one-way ticket. It runs from 6:00 to 22:55 approximately. There are free shuttle buses connecting terminals T1-T2-T3 and T4.

By metro/train: Not recommended. The trip takes 1 hour and 20 minutes and you will need to pay different tickets for metro and Cercanías.

By taxi: from the Airport to UAM the trip should cost around 35 EUR, and take no more than 20 min (without  traffic jams). The exact address for the taxi driver is "Facultad de Ciencias, Universidad Autónoma de Madrid, Campus de Cantoblanco".

... the Universidad Autónoma de Madrid from Madrid City Center

By train: The trip takes around 15-25 minutes in Cercanías (local train). Take Cercanías line C-4 towards Alcobendas/San Sebastián de los Reyes or Colmenar Viejo in any of the main stations in Madrid (Atocha, Sol, Nuevos Ministerios, Chamartín). The destination is "Cantoblanco, Universidad Autónoma". The fare is 1,85 EUR / one-way ticket. The last train from Cantoblanco to Madrid departures at 00:12. 

By bus: The trip takes around 15 minutes from Plaza de Castilla (without traffic jams). From this station (you can reach Plaza de Castilla by metro) you take any of these lines entering Cantoblanco campus:

714 Madrid (Plaza de Castilla) - UAM

827 Madrid (Canillejas) - Alcobendas - U. Autónoma

828 Madrid (Canillejas) - Alcobendas - Univ. Autónoma

...  Madrid City Center from the Adolfo Suárez-Madrid-Barajas Airport

By train: Cercanías line C-1 connects the terminal T4 with the city (Chamartín, Nuevos Ministerios, Recoletos, Atocha). The trip takes 15-25 minutes and the ticket costs 2,60 €. You can change in Chamartín and/or Nuevos Ministerios towards Sol station without an additional cost, the same ticket is valid (here you can find the location of the Cercanías station at the Terminal T4).

By metro: Take the metro line 8 towards Nuevos Ministerios station (exact location of the subway station at the Terminal T2 (here) and at the Terminal T4 (here)). The trip takes 15-25 minutes and the ticket costs 4,50-5,00 €.

By taxi: from the Airport, there is a fixed fare of 30 €.