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The second most important Madrid train station is Chamartín, and it is located towards the north. It hosts the railway routes connecting Madrid and northwestern Spain, a couple of AVE routes, and some Cercanías lines, plus the international line to Lisbon.
Contrary to Atocha, Chamartín is a fairly modern station built in the 1970s and then refurbished later on. It is mainly used as a transport hub inside the city. But it is also the departing station of the AVE high-speed train to Segovia.
Despite its smaller size, it has all the services a train station usually has, including cafeterias, restaurants and shops.
It also has a left luggage service, located outside the main building. If you exit the station through the main entrance, walk left and look for the consignas signs.
Chamartín is in the north of Madrid. The exact address is c/ Agustín de Foxá, 40.
There is a Metro station inside the premises, Chamartín, accessing to lines 1 (light blue) and 10 (dark blue).
While you could use Metro line 1 (light blue) to go to Atocha, it will take you much longer than catching a Cercanías train with 6 different lines serving the route: C-1 (light blue), C-2 (dark green), C-3 (purple), C-4 (dark blue), C-7 (red) and C-10 (light green).
Read more about purchasing a Cercanías train ticket.
Unfortunately, there are no Metro direct routes from Barajas airport. Therefore if you have lots of luggage it might be preferable to use an alternative. In fact, Chamartín is very well connected to Barajas airport thanks to Cercanías line C-1 (light blue).
Obviously, you can also get there by bus (lines 43, 72) and taxi.
You can read more about getting to Madrid by train.