Official Web page of the Royal Alcázar of Seville has detailed information about the architecture and gardens, a blend of Mudéjar, Islamic/Moorish, and Renaissance elements.
The address: Casco Antiguo, 41004 Seville, Spain.

For a visit you need to make a reservation, and be on time at the entry point Puerta del León (Gate of the Lion). The staff will check your ticket and the assigned time slot. The Spanish are very formal about these rules. Tickets are limited, so reserve ahead of time for the days of your visit. The premises are huge. Plan to spend several hours just to take a glimpse of the things.

A side note for the fans: Parts of Game of Thrones were filmed in these gardens.

Wikipedia article about the Seville Real Alcázar