The Real Alcázar sits on the site of a 10th-century Almohad fortress. When Ferdinand III took Seville from the Moors in 1248, he moved in rather than tear it down. A century later Pedro I of Castile, working with Muslim craftsmen from Granada, built the Mudéjar Palace that is the reason you're booking the ticket — horseshoe arches, carved stucco, azulejo tiles, and the Patio de las Doncellas, one of the most beautiful courtyards in the world.
Successive kings added: Gothic halls after Pedro, Renaissance galleries in the 16th century, Baroque chapels later. The whole complex is the oldest royal palace in Europe still in use — the Spanish royal family lives here when they visit Seville, which is why the upstairs Cuarto Real Alto has separate, timed, guided visits.
Outside the palaces, the gardens are the real surprise: 7 hectares of Moorish pools, cypress walks, orange trees, peacocks, and hidden pavilions. Allow at least an hour for the gardens alone. The whole complex absorbs a half-day if you want to see everything.