Feed back on this itinerary much appreciated

I never understand why people do this kind of itinerary. Why go into Madrid twice? I visit Spain a few times year, flying out of JFK or, in March, from Miami.

Fly from the US to Sevilla with a connection in Madrid and your checked luggage checked through to Sevilla.
Spend your time I Evilla and Cordoba and then, train to Madrid, spend your time there, and fly home from Madrid.

Or, the reverse: Fly to Madrid, take train to Cordoba, See Cordoba, Take train to Sevilla and spend time there, then fly home from Sevilla with a connection in Madrid.

I prefer flying Iberia but you can also check American. You can book both on the Iberia.com site.

Assuming you've already got your flights booked and can't change them, the previous poster's suggestion is moot. In that case, when you land in Madrid, take the bus to Atocha station and go directly to Seville.

You have ten nights. I recommend 4 in Seville, 2 in Córdoba, and 4 in Madrid. At the very least least spend one night in Córdoba.

But how you break up your ten nights depends largely on what you're interested in seeing and doing in each city.

Sometimes, especially when traveling by rental car, a circular route beginning and ending in the same city is optimal. Just saying…

On a trip to Madrid, Cordoba and Seville, a rental car would be much less efficient than the high-speed trains. It's not a close call, either.

As for flying in and out if Madrid, that sometimes saves a great deal of money. For me in 2019, flying into Madrid rather than one of the Andalucia airports saved $500; the return was from Barcelona. I figure posters checked the air fares and made a rational choice for their origin airports. (True, it occasionally turns out a poster didn't know about the "multi-city" flight option and priced two one-way tickets.)