The remains of the old Muslim fortress that gave the town its name, partially rebuilt in the 14th and 15th centuries.
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Universidad Complutense
Founded in 1499 by Cardinal Cisneros, and the centre of academic excellence in Spain in the 16th and 17th centuries. Visit by guided tour only, hourly in Spanish, in English at 14:00. The tour takes in the ornate plateresque façade, the three interior patios, the mudejar chapel, and the Paraninfo auditorium where the Cervantes Literary Prize is presented by the King annually on April 23. The university goes back to an older institution that did not teach the full range of subjects of a "proper" university founded in the 13th century and was moved to Madrid as the modern day Complutense University in the 19th century. In the 20th century a new university was founded in Alcalá.
Dating back to 1602 and thus older than Shakespaere's "Globe" in London it claims to be one of the world's oldest theaters even though it hasn't been in use as such without interruption. Both guided tours and plays are on offer.
A 15th-century charity hospital, probably the oldest in Europe in continuous use. Nowadays it's a care home for the elderly.
Cervantes birthplace
This is the house where the famous author of El Ingenioso Hidalgo don Quijote de la Mancha was born in 1547, and lived his early days. The museum recreates life in a Spanish house of that period, though perhaps a more stable, prosperous household than Cervantes' own. His father was a barber-surgeon, so the old shaving & blood-letting bowl foretells Don Quixote's mad helmet. The book was widely translated soon after Part One was published in 1605, and there's an impressive collection of translations and other books and manuscripts from around the world. Free admission but to avoid overcrowding they only let in a dozen or so at a time, so there may be a queue.
The museum is housed in the 17th-century Madre de Dios monastery-college on Plaza de las Bernadas. Prehistoric and Roman finds from the area.
Lonja de la Magistral
It was built in the 15th century, but rebuilt after fire damage in 1939. It's called a "magisterial" cathedral because its clerics were all masters, ie graduate teachers of the university. Contains the Cripta de los Santos Niños a reliquary dedicated to two children who were supposedly executed for their Christian faith under emperor Diocletian allegedly also containing their mortal remains. It's also Cardinal Cisneros' site of burial although his much more elaborate tomb is found in the Chapel of San Ildefonso on University grounds.