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Connecting at MAD / Madrid Barajas International Airport
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Terminals include

Terminal 1: International. Star Alliance primarily (also the only non-Schengen area outside of T4)

Terminal 2: Domestic mostly. SkyTeam primarily

Terminal 3: Schengen and some Domestic mostly. Air France/KLM/Lufthansa usually leave from here, but really it's just a slight extension on T2

Terminals 1-2-3 are adjacent and host Star and SkyTeam alliances and are all connected airside.

Terminal 4: one world including Iberia
Domestic and Schengen mostly from Terminal 4
International from Terminal 4-S (satellite) (Except IB or I2 operated flights to UK and Ireland as well as BA CityFlyer flights to LCY that operate out of T4 Main, though note that usually one IB flight to LHR daily is operated by an A330 or A340, these flights go from T4-S).
Both connected by an underground train, though going from T4-S to T4 requires going landside and re-clearing security in order to access T4.

Terminals are connected by a landside shuttle bus service.

Connecting from non-Schengen to Schengen (or departing the airport) one must process immigration in T-4S. Queues can be lengthy at times; if you are an EU citizen, you wil lfind the kiosk to your right in the queues. If you are not, keep to the right of the general queues anyway, as the EU queues can empty and they begin waving non-EU passengers into the EU lines.

The train connecting the T4-S satellite to T4 must be accessed via lifts or stairs; the lifts are faster. A non-Schengen to Schengen connection can take an hour or longer - A 1.5 hours is recommended as minimum connect times, and possibly more for Schengen to non-Schengen if during busy hours due to security procedures, particularly for US flights. Status passengers on Iberia flights to the US have access to a separate priority queue to clear the extra US screening.

Connections to other terminals are by a landside shuttle bus located, and can take rather longer than one might think as T4 is quite far away from T1/2/3. There is a metro link between the two, however you will have to pay full fare and even for a single rider a taxi is pretty competitive on price when the airport supplement is included.

Resources:

Link to Madrid Barajas Airport (World Airport Guides)

Link to AENA official MAD Madrid Barajas website by airport operator AENA

Wikipedia decent article on Madrid Barajas (with listings of airline gates and terminals - BUT caveat - it fails to differentiate between Terminal 4 and Terminal 4-S!)

Schengen Agreements nations information (with maps, etc.)