I bought my plane tickets from American Airline, because I wrongly thought I should only buy plane tickets from a United States-based airline. I was originally going to travel in October, but I rescheduled my trip for March. Originally, I was going to take flights from Detroit to Seville. or Detroit to Granada. When I convinced the airline staff to let me change my travel dates, the trip with flights ending in Granada was not available anymore, the trip to Seville required changing planes in Madrid with less than 2 hours to change planes. I figure I am just as well off taking the train from Madrid to Seville than trying to get my passport stamped and switch planes in a hurry at the airport in Madrid. Maybe I was wrong. If I had bought plane tickets from Tap Portugal or another airline, I could have arrived by plane in Granada or Seville without first changing planes in Madrid. My reason for not going to Toledo right after arriving in Madrid is because the two former synagogues that are museums now, are closed on Mondays and/or Tuesdays, and I doubt whether I would arrive in time to see them on the Sunday I arrive.
If I take the bus from Seville to Granada, the bus will go far south of Cordoba, which won't seem like backtracking, and it should be cheaper than the train and not significantly longer. Unless I am wrong.
I am thinking of buying my first train ticket in advance. I don't want to find out at the last minute that I have to find a place to spend the night in Madrid and try changing my itinerary, at the last minute, because I can't buy a train ticket to Seville at the last minute on the day I arrive.