Final answer:
The Persian Empire first conquered Ionia, a territory of Greek city-states along the Aegean Sea coast, during Cyrus the Great's reign in 546 BCE. This early interaction set the stage for the later Persian Wars between Greece and the Persian Empire.
Step-by-step explanation:
The first Greek territory conquered by Persia was Ionia, which was located along the coast of the Aegean Sea in what is now western Turkey. During the reign of Cyrus the Great in 546 BCE, the Persians invaded Anatolia, overthrew the kingdom of Lydia, and swiftly defeated the Greek city-states (poleis) in Ionia.
Despite their conquest, the Persians allowed the Ionian Greeks to maintain their language, religion, and culture, requiring only loyal warriors and taxes.
The Greeks in the colonies generally did not find Persian rule oppressive since they were permitted a degree of autonomy under Greek leaders who were appointed as governors by the Persians.
Later, conflicts between Greece and Persia escalated. Following the Ionian Rebellion and Athens' support of it, the Persian king Darius sought to punish Athens, eventually sparking the Persian Wars (492-449 BCE). Over time, these conflicts had significant impacts on both empires, with Greece achieving victories and Persia retaining strong influence in the region despite setbacks.