How to get to Madrid
By plane (most convenient if coming from outside Spain):
Madrid has a single airport, Madrid-Barajas (MAD), with numerous connections around the world, being among the largest airports in Europe. It has 4 terminals, with T1, T2 and T3 very close one to another, being T4 slightly separated (there is a free bus connection running continuoulsy among terminals).
Airport to the city:
Taxi: There is a flat rate of 33E from the airport to the city centre (or back). The city centre is delimited by the M-30 road (e.g. Atocha, Sol, Nuevos Ministerios, Chamartín), which does not include the UAM Campus.
Metro: Excluding taxi, this is probably the easiest, most versatile and frequent travel mean. All airport terminals are connected to the Metro Line 8, connected in turn to the wider Metro network. This connects to the Nuevos Ministerios transportation hub, from where one can easily reach UAM Campus and to Metro lines L10 and L6. A single ticket costs ~5E.
Cercanías Train: At the airport there is only connection to Terminal T4. Low frequency but fast moving. Two stops minimum are necessary to get to UAM campus.
Bus: There is a 24h bus to the airport to the city centre (Atocha). Single ticket costs 5E.
Airport to UAM Campus:
Taxi: This will only be 15min, but the flat-rate does not apply here.
Bus: Check timetables and trajectories for buses 827 and 828. These are lines connecting directly the airport (from Terminal 4) to UAM Campus The bus stop at UAM Campus is "Newton-Nicolás Cabreras". At the airport there is a unique stop for both directions, either Madrid or UAM Campus, so it is convenient to ask the driver whether the bus goes to Universidad Autónoma.
Cercanías Train: The C-4 train line connects Nuevos Ministerios to UAM. From the airport you can get to Nuevos Ministerios using the train (C1, C10 from Terminal T4) or the Metro (L8, from all Terminals).
By train (if you travel from elsewhare in mainland Spain):
There are many connections either high-speed or with conventional trains. Most trains are operated by Renfe, the national trainline company. Recently, other low-cost companies started operating some of the main lines (avlo, ouigo).
Tips on getting to UAM Campus
With Cercanías Train: Take a train direction either Colmenar Viejo or Alcobendas-San Sebastián de los Reyes (C4). Get out at Cantoblanco Universidad stop. From here there is a 15min walk to the IFT building. Here a map of C4 line.
With Intercity buses (the station is underground): 714 (Plaza de Castilla - UAM - Universidad de Comillas); link (in Spanish).
Tips on moving around the City
Metro : Madrid has an extensive and convenient Metro network (map) connecting most places in town, including the Airport. But it does not reach the UAM campus. You need to purchase a Metro transportation card (~2.5E), unfortunately not valid for the Cercanías train. You can fill the card with single tickets (1.5-2E each), 10x tickets (12.20E), airport ticket (5E) or airport supplement (3E). The 10x tickets for zone B1 costs 6.10E and is valid to go from Plaza Castilla to UAM Campus. More information here. The prices might vary (in fact being lower) due to recent financial support measures by the regional goverment.
Cercanías Renfe: These are local trains running regularly within the province of Madrid. Tickets can be bought at stations either from a machine (accepting cash, notes, bank and credit cards) or from a ticket office. There is a zone system, most of the centre is in Zone A, the UAM Campus in B1. If staying in Madrid downtown, bying a 3-zone 10-Journey ticket is recommended. Single tickets (for 3 zones) cost 1.85E, and 10 trip cards, 13.70E; see here.
New! There is a new card for 10E, valid May 1st -July 31st, that can be used throughout the whole Cercanias network. It can be purchased at expenditure machines with the help of personnel.
Taxi: Taxis are numerous and for European standards, reasonably priced. Cabify and Uber are also available in Madrid.
Buses: There are two type of buses, the local ones from EMT (red or blue) and the Interurbanos (green). For the EMT buses you can use the same ticket as for Metro. The Interurbanos require a different kind of ticket, usually bought on the bus. Most bus drivers do not accept notes bigger the 5E.