Madrid to Cordoba by train

Book early and save: Yes

Online bookings open: up to 6  months ahead of the travel date - depending on the time of year.
The online booking window can be shorter between late July and early October.

When looking up journeys (not travelling) between late July and early October, it's likely you won't be able to book for journeys beyond the second Sunday in December.

On this route, prices are set per departure according to demand; hence the lack of price info below.

It can pay off to be as flexible as possible regarding departure and arrival times, because for these trains on this route it’s not unusual for a few departures to be available at much cheaper price, regardless of how far ahead you will be booking.
The limited numbers of tickets released for sale at very cheapest prices also inevitably sell out, so if possible book more than a couple of months ahead and you’ll be more likely to find them available.
Though from the moment the tickets are placed on sale, some departures will be cheaper than others.

Whether you will be travelling on an AVE or Alvia train doesn't affect the ticket price, some AVE departures can be cheaper than the Alvia trains and vice versa.
Also the IC trains can be more expensive, despite being slower.

Seat Reservations:

Seats will automatically be assigned when booking tickets for this journey.

Rail Pass Users:

Rail pass users will need to pay reservation fees prior to boarding these trains - on this route, with its fairly frequent departures, you may as well book these reservations at the station when you arrive in Spain.

Don't target travelling by the Alivia trains in the expectations of making a saving; the rail pass reservation fees on the Alvia trains are usually cheaper, but not on a route shared with AVE trains, such as this one.
Though taking an Inter City train will be a cheaper option.