Which caliph's Cordoba library allegedly held 400,000 volumes?

Al-Hakam II, who ruled Córdoba in the tenth century and sent agents across the Islamic world to buy or copy anything worth having. The figure of 400,000 is a chronicler's, and probably not literal, but tenth-century Christian Europe's largest libraries held a few hundred books, so the gap is real whatever the exact number.

He is said to have read the books, annotated them, and employed copyists, binders and at least one woman as a scribe. Córdoba at that point had street lighting, running water and public baths, and the city functioned as the route by which Greek philosophy, Indian mathematics and Persian astronomy reached Latin Europe - largely through Toledo's translators in the following century.

The library did not survive its owner by long. Al-Hakam's successor was dominated by a chief minister who, needing the approval of religious hardliners, had the philosophy and astronomy sections publicly burned; the remainder was scattered during the civil wars that broke the caliphate apart after 1009. The estimate of what was destroyed is unverifiable, which is rather the point - the loss includes the record of what was lost.