Of course, in both cases we have the Argüelles metro station (lines 4, 3 and 6), which is just 200 meters from the Puerta de Muralto. To get there from the Adolfo Suarez Madrid Barajas Airport, you must take metro line 8 in any of the Terminals in the direction of Avenida de América station, where you must change to line 4 (Argüelles - Pinar de Chamartín, brown color) at direction Argüelles.
If you arrive in Madrid by train, from Atocha station you can also take metro line 1 (blue) towards Sol, where you will change to line 3 (yellow) towards Argüelles station.
And if the destination station is Chamartín, also take line 1 (blue) towards Bilbao station, where you must change to line 4 (brown) towards Argüelles station.