Which Chinese dynasty was established by Kublai Khan?

Kublai Khan established the Yuan dynasty. He proclaimed the dynastic name Great Yuan in 1271, creating a Chinese-style imperial dynasty for his Mongol-ruled realm.

Kublai was the grandson of Genghis Khan and became Great Khan in 1260 after a civil war with his brother Ariq Böke. Unlike earlier Mongol rulers, he increasingly centred his government in China and adopted institutions, ceremonies, and political language associated with Chinese dynastic rule. The name Yuan came from a passage in the Chinese classic I Ching.

The Yuan conquest of China was not complete when the dynasty was proclaimed. Kublai’s armies defeated the Southern Song in 1279, making him the first emperor from a non-Han ethnic group to rule all of China proper. The dynasty lasted until 1368, when the Ming dynasty seized Dadu.

The main mix-up is calling the Yuan simply the Mongol Empire. The Yuan was the Chinese dynasty founded by Kublai, while the wider Mongol Empire had already fractured into several khanates.