Upvote:4
There's the C1 train that goes from Barajas' Terminal 4 to Atocha.
I don't know if this is still vald, but if you already have your AVE train ticket, then you get a free pass on the C1:
http://www.accesrail.com/pdf/MAD-airport.pdf
This would be the simplest and cheaper way to do it.
From Atocha, take the AVE to Sevilla.
Upvote:4
The AVE seems around $66 and 2-1/2 hours. Flights seem to start at around $43 and 1 hour, though timings might not suit.