Should I buy train tickets Madrid- Cordoba in advance or on arrival day?

I would buy an AVE (fast train) ticket online ahead of time. The ticket counter at Atocha can be very crowded, unless you use a kiosk, and then that can be confusing. You are fine with the second class ticket on the AVE. If you have this ticket in hand, then the commuter train from the Madrid airport to Atocha should be free. It's worth going on the AVE. There is maybe only one stop between Madrid and Cordoba. An 11 AM train should give you plenty of time. I've done every scenario, and this is the best way. You can't buy the AVE ticket too far ahead, though---maybe now is the earliest.

Thank you Linda. I will buy in advance then.

Irene,

Generally, it's not recommended to book train tickets in advance on day of arrival due to possible delays with your plane or at the airport.
As you already know, there are frequent trains to Córdoba from Madrid, & they seldom sell out, except for the ALVIA trains which are generally less expensive than the AVE trains on this route.

Having said this, if you do choose to buy a discounted ticket in advance, then 11AM seems like a good cushion of time.

Worse case scenario, if your plane is delayed or passport control lines are huge, you'll have to buy another ticket at full price.

If you decide to wait to buy your tickets upon arrival, you can easily buy them at the airport, there's no need to wait till you arrive to Atocha's train station.

Keep in mind that you can travel on the Cercanias train (from/to airport to/from Puerta de Atocha train station) for free if you purchase an AVE ticket.
You can take the C-1 Cercanias from Terminal 4 & you'll arrive to Atocha's station in around 25 minutes.

As a side note...If you plan to visit Granada on your trip, make sure you book your tickets to the Alhambra way in advance.

Enjoy your trip!

Thank you Priscilla, this is a very good info about buying tickets at the airport.
And yes, I am going to Granada, Alhambra tickets booked!

Irene,
It's good to hear that you've booked your Alhambra tickets already!

When my mom & I visited Granada (October 2015), we encountered many disappointed tourists without Alhambra tickets.

If you decide to book your train tickets (Madrid>> Córdoba) in advance (to save money), you will still need to print your Cercanias train tickets at the airport, either at the automated ticket machines, or at the Renfe office.

You may want to read point #8, labeled, The “Combinado Cercanías”, on this helpful website for more information and specific details about obtaining your Cercanias tickets.

Madrid's Atocha train station is huge & I found it a bit challenging, especially since I was experiencing jet-lag.

Here is a schematic diagram of Atocha's train station.

Take Priscilla's good advice. For me, it's not worth the savings on an advance ticket to risk missing the train or to end up sitting around the airport or train station for ages.

When you get to the Renfe office, they will sell you a ticket for the first train that you can catch, considering the Cercanias schedule and transfer time at Atocha.

Thank you very much everyone. This is very helpful info.

We bought in advance and it was much cheaper. For a ticket you need the day of arrival, I would not risk it though unless you are very comfortable letting the advanced ticket go and buying a new one if you miss the train.