In 750 the Abbasids overthrew the Umayyad caliphate in Damascus and killed nearly every adult male of the dynasty. One who escaped was a grandson of Caliph Hisham in his early twenties — Abd al-Rahman. For five years he fled across Palestine, Egypt, and North Africa to reach the relatives of his Berber grandmother. From there he crossed into the Iberian Peninsula, in Muslim hands since 711 but fractured by internal conflict. In May 756 he defeated the local governor at Córdoba and was proclaimed emir. It was the founding of an independent Islamic state that did not recognise the caliph in Baghdad — the Umayyads of al-Andalus.

Later generations turned the emirate into a capital. In 929 Abd al-Rahman III formally took the title of caliph; Córdoba was now a third Islamic centre rivalling Baghdad and Cairo. By the middle of the 10th century Córdoba was probably the largest city in Europe: a population in the hundreds of thousands, oil lamps lighting the streets at night, water piped into homes, paper mills. The library of Caliph al-Hakam II approached 400,000 volumes — while the richest Christian monastery libraries of the era held a few hundred manuscripts.

Science and philosophy settled in. Ibn Rushd (Averroes) wrote his commentaries on Aristotle here; Maimonides was born in Córdoba; al-Zahrawi compiled his catalogue of surgical instruments; al-Zarqali drew up his astronomical tables. Muslims, Jews, and Christians lived in the same cities, traded in the same markets, translated in the same workshops. This is the situation often called "convivencia" — coexistence — and it is contested: the sources show daily cooperation, but also tension, fiscal burdens on non-Muslims, and intermittent violence. Even so, nowhere else in Europe was there contact among three faiths at this scale.

In 1031 the Caliphate of Córdoba collapsed into civil war; the age of small taifa kingdoms began. Toledo fell to Christian forces in 1085, and the Arabic manuscript heritage there started to be translated into Latin. Europe re-learned much of Aristotle not from Baghdad but from al-Andalus, through commentaries that passed from Arabic into Latin. By 1492, when the fall of Granada ended Muslim rule in Iberia, the peninsula's language, architecture, and mathematics had been permanently marked.