We will be taking the train from Cordoba to the Madrid airport on our last day in Spain. There are trains all day so we were hoping to get one of the evening trains from Cordoba and go directly to the airport. Have hotel booked there for a very early flight out the next morning. I'm not finding a train that goes from Cordoba to the airport. Is it necessary to change at Atocha? Or perhaps there is another train station in Madrid that would work better for transfer to the airport? So my questions are: is there a direct train from Cordoba to Madrid airport?? If not, which train station would be most convenient for transferring from Cordoba train to airport train??? OR, is there even any choice??? Thank you for your help!!!!

Atocha, where trains from Cordoba arrive has a direct metro to Madrid Airport - no direct trains - simple transfer to metro at Atocha.

http://www.accesrail.com/pdf/MAD-airport.pdf

This explains how to connect Atocha to airport and says if arriving by AVE train you get a free ticket from Atocha to the airport - see instructions in link above.

no direct Metro line from Atocha to the airport, you have to make a change.
If you you are going to T4, you can take a commuter train..Cercania direct from Atocha
to T4.
there is a bus from Atocha to all terminals.

There are no hotels at Adolfo Suárez Madrid-Barajas Airport. What 'airport' hotel did you book? There are hotels in Barajas and between the airport and Madrid, which would not be my option for spending my last night in Madrid.

The trip from the center of the city to T4 takes around 25 minutes in communter traffic and the taxi rate is set at 30€.

Thank you all for the helpful information....just what I needed!!