It is not possible for me to provide a detailed account of every important event that happened in the 6th century AD, as there were many significant developments across the world during this time. However, here are some of the major events that occurred during this period:

- 500 AD: Prince Shotoku of Japan issues the Seventeen-article Constitution, which outlines principles for governing Japan based on Confucian and Buddhist principles.

- 507 AD: The Battle of Vouille takes place in France, leading to the defeat of the Visigoths by the Franks and the consolidation of Frankish power in the region.

- 529 AD: The Academy in Athens, Greece, founded by Plato and Aristotle, is closed down by Emperor Justinian as part of his efforts to suppress paganism and promote Christianity.

- 532 AD: The Nika Riots take place in Constantinople, Greece, with factions of chariot racing fans rioting and causing widespread destruction in the city.

- 535-536 AD: A mysterious atmospheric event causes a "year without summer," leading to crop failures, famine, and other disasters in Europe, North Africa, and Asia.

- 541-542 AD: The Plague of Justinian spreads throughout the Byzantine Empire and beyond, killing an estimated 25 million people.

- 570 AD: The Prophet Muhammad is born in Mecca, Arabia, founding the religion of Islam.

- 589 AD: The Sui dynasty is established in China, reunifying the country after centuries of division.

These are just a few of the many important events that took place in the 6th century AD, and there were many others that shaped the course of history during this period.