What is the most efficient routing?

Looking at the train route maps on the Renfe site, there are direct trains between Seville and Granada and between Madrid and Granada. There is also a bus route between Madrid and Granada. Cordoba is on the train route between Madrid and Seville, so . . . . Madrid - Cordoba - Seville - Granada - Madrid or the reverse.

I'd start planning by looking at the train/bus schedules to/from Granada and work from there. There are few trains on those lines, while there is frequent service between Madrid and Cordoba/Seville, so it's easier to put Granada "in place" and then work out the rest.

And Granada is the place where you MUST make reservations for the Alhambra -- then plan your trip around that date.

Most efficient is to fly into/out of Madrid and Granada. Check price options to decide which. If nothing else fly round trip to Madrid but get a Vueling flight to or from Granada at one end or the other. It's not a bad idea to check Alhambra reservations, they may drive your itinerary.

Everything else is convenient by train Madrid to Cordoba (stay a night if you have it), Cordoba to Sevilla, Sevilla to Granada (or reverse depending on your flight plans).

If you want to do side trips, check the bus stations. Not only do they do cheap rides between towns but they run a lot of day trips. Everything that includes a bus is a good value and never needs reservations (I like to pick up tickets the evening before so I have can schedule the next day).

Me again.

Thank you for the replies.

Does this make sense? Starting and ending in Madrid ...

Train to Seville/Stay in Seville as a home base for four nights.

Tour Seville.

Train or Bus to Granada for The Alhambra (day trip returning to Seville at night).

Train or Bus to Cordoba for the Mezquita (day trip returning to Seville at night).

Train back to Madrid.

Thank you!

No, I would go Madrid, Cordoba, Seville, Granada then back to Madrid.

Train from Madrid to Cordoba, Train from Cordoba to Seville. maybe Bus to Granada, not sure about Granada Madrid.

Alsa is the bus company to look at: alas.es

Renfe is Train: renfe.es
I found the Renfe website hard to use as it is primarily in Spanish. Good luck!

Sally, I apologize for not thanking you sooner ... it all worked out well and I am grateful for your post guiding me on how to plan our route efficiently.