The cheapest way to get from Seville Airport to the center is to take the EA bus line that leaves you at the Plaza de Armas in just over half an hour for 4 or 6 euros, if you take the return ticket.
These buses leave every 15 or 30 minutes, depending on the time, from 5:30 a.m. to 1:25 a.m. from a stop located in front of the arrivals terminal.
If you make the trip in reverse, you will have to take the bus from the Plaza de Armas, located 15 minutes walk from the Cathedral, which leaves every 20 minutes from 4:30 a.m. to 12:30 a.m.

At the exit of the arrivals terminal you can take a taxi at the official rank that will take you from the airport to the center of Seville in about 20 minutes.
The fixed price of the taxi is 22.81 euros from Monday to Friday from 7 a.m. to 9 p.m., while on weekends and other hours it rises to 25.43 euros.
Keep in mind that if you travel during Holy Week or the April Fair, and take the taxi between 9 a.m. and 7 a.m., the price will rise to 31.78 euros.