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A taxi from the airport to the city centre costs a fix fare of 20.70€ (23.08€ on weekends).
A metropolitan bus service is also available for 2.30€.
Other alternative airports close to Seville are the following: Jerez (XRY, 85km far away ), Málaga (AGP, 195km) and Faro (FAO, 200km).
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By coach: A much cheaper way to get to Seville from Madrid is by regular coach service: the roundrip is just 35€ but the bus journey is more than six hours. Nonetheless, it can be convenient for flight connections since some of the depart from and arrive to Madrid Airport (Barajas, MAD). The schedule can be found here.
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Metropolitan transportation system
An extensive public transportation bus network covers the whole of Seville Metropolitan Area: see its official web site here (in Spanish).
Bus line 34 have two stops in the Campus of Reina Mercedes and drives you directly to/from the city centre.
As well as single tickets (1.20€ each), which can be bought on the buses, there are 1 and 3 day travel cards (4.50€ and 8.50€ each, both of them can be bought in stationeries all over the city).