Caliph al-Mansur builds the 'Round City' of Baghdad as the Abbasid capital; it soon becomes one of the world's largest cities.
A movement rising from Khorasan defeats the Umayyads at the Battle of the Zab, establishing the Abbasid Caliphate.
At Baghdad's House of Wisdom, al-Khwarizmi writes his treatise on completion and balancing, founding algebra as a discipline; the word "algebra" derives from its title.
Under Caliph al-Ma'mun the House of Wisdom becomes a centre of translation and scholarship, preserving and extending Greek, Persian and Indian learning.
Caliph Abd al-Malik completes the Dome of the Rock, one of the oldest surviving works of Islamic architecture.
Husayn ibn Ali, grandson of Muhammad, is killed by Umayyad forces at Karbala, an event central to Shia Muslim memory.
Muawiya I establishes the Umayyad dynasty with its capital at Damascus, making the caliphate hereditary.