Which dynasty preceded the Ming in China?

The Yuan, which was Mongol - Kublai Khan's dynasty, the first time all of China was ruled by outsiders. It lasted less than a century, and the Ming that overthrew it in 1368 defined itself substantially against it.

The Yuan ran China with a formal ethnic hierarchy, placing Mongols first, then Central and West Asians, then northern Chinese, then southern Chinese last - and staffed the administration heavily with foreigners rather than with the Confucian scholar-officials who had run the country for centuries. That is why Marco Polo's account, if it is genuine, describes a European finding employment in Chinese government: it was a period when that was possible.

The Ming reaction shaped everything after. It restored the examination system, rebuilt the Great Wall in the form tourists now visit, and after the enormous treasure voyages of Zheng He - fleets far larger than anything Europe had, reaching East Africa decades before Columbus sailed - abruptly ended them, burned the records and banned oceangoing shipbuilding. China withdrew from the sea at exactly the moment Europe went out onto it, and the reasons were budgetary and factional rather than any failure of capability.