Final answer:
The empire founded in the 1300s that spread into Europe, Africa, and Asia was the Ottoman Empire, established by Osman I.
Step-by-step explanation:
The empire founded in the 1300s by a Turkish leader and which expanded into Europe, Africa, and Asia is the Ottoman Empire. This empire was established by Osman I in 1299 and saw significant expansion during its early stages. The Ottoman Empire inherited the Muslim leadership from the Abbasids and after conquering Constantinople in 1453, which marked the end of the Byzantine Empire, it became a dominant power in the region. Over the centuries, under leaders like Suleiman the Magnificent, the empire encompassed vast territories in Europe, Africa, and Asia, including the Balkans, North Africa, and parts of eastern Europe.