Train schedule from Sevilla to Granada for morning of June 15; RENFE website frustrating

I cannot grasp what your problem is but the morning direct journey departure and arrival times are -
0640 - 0957 1155 - 1507

Additionally, with one change, 0650 - 1055 and 0950 - 1330

You may want to also consider bus - www.alsa.es

As the earliest you will be at the Alhambra will be mid to late in the morning and there are only two 'sessions' morning and afternoon, it would have to be afternoon purchase.

Book an afternoon Alhambra ticket and take the bus. The bus has a lot more times (about hourly) and takes the same amount of travel time. About the same price or a little cheaper. You can buy your bus ticket that same day or a day in advance when you arrive in Sevilla.

Bus is a fine plan, with more direct departures per day. June 15 is the first day of the new trains schedule in most of Europe. I am finding slightly different options than what Neil reported, e.g., I don't find a 9:57 departure reflected on Renfe, Rail Europe, or DB, but do see the 11:55 departure for sale. The 6:40 departure is listed by DB (which is not a sales agent for Spain), so I would expect it to run, but tickets don't appear to be for sale online right now.

laura and 'I am finding slightly different options than what Neil reported, e.g., I don't find a 9:57 departure' - please re-read and perhaps not clear - 0957 is an arrival time.