By the year 750, the Islamic world had begun to fragment into separate kingdoms, or caliphates. The most powerful caliphate was centred in Baghdad. A year before, the Abbasid family (descended from Abbas, the uncle of Muhammad ) had supplanted the Umayyad family and begun a reign that would last almost five centuries. During the early years of the Abbasid caliphate, Baghdad was the centre of one of the great flowerings of human knowledge. Theologians, philosophers, poets, and doctors gathered in Baghda d to study at the "House of Knowledge". They translated Greek classics into Arabic, studied Indian mathematics, learnt about paper from China, and explored Buddhism. Subsequently, Arab scholars throughout the Muslim world from Cordoba to Cairo to Samarqand corresponded with each other. At Cairo, the Arabs founded an institution during the 9th century that is often described as the world's first university. Baghd ad eventually fell to Turkish invaders, who adopted the Muslim faith; later, in 1258, it fell to the Mongols.

In Islamic, or Moorish, Spain a separate Umayyad dynasty was established in 756, led by the only survivor of the bloodbath that followed the rise of the Abbasid dynasty in Baghdad. In 929 Abd-ar-Rahman III proclaimed himself caliph, and so challenged Baghdad's leadership of the Muslim world. Moorish Spain was a centre of learning and strongly influenced Christian Europe. Cordoba had a library with 400,000 volumes. The Spanish Moor Al Hassan pioneered the study of the human eye, and Abu Kasim wrote the first illustrated text on surgery. Medical education in Europe had its origins in Muslim Spain.

During the 15th century, in a kind of internal crusade, Spanish Christians slowly pushed the Moors from Spain; the last Islamic stronghold, Granada, fell in 1492. This "reconquest" allowed the Christian rulers Ferdinand V and Isabella I to turn their attention to supporting an explorer named Christopher Columbus, who claimed he could reach Asia by sailing across the Atlantic.

Other Muslim kingdoms were established in Asia and Africa. In 999 Mahmud of Ghazni established a Turkish Islamic empire in Afghanistan. His court at Ghazni was another centre of culture. Under Mahmud, the Turks frequently raided northern India, and eventually that region entered the Islamic orbit. Between 1206 and 1526 the Delhi Sultanate, ruled by Turkish Muslims, controlled much of India. Muslims also pushed into sub-Sarahan Africa, where they conquered Nubia and other African states. The kingdom of Ghana fell to the Muslims in 1076. Soon mosques appeared deep in Africa.

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