Alexander's military journey redrew the boundaries of the ancient world. In 334 BCE he crossed the Hellespont, in 333 he defeated the Persian king Darius III at Issus, in 332 he took Egypt (where Alexandria was founded), and in 331 he broke the Persian army decisively at Gaugamela. The following years carried him from the Iranian plateau into Central Asia and on to the northwestern edge of India. There, on the banks of the Hyphasis, his men refused to march further east. He died in Babylon at thirty-two on the return.

He had been a student of Aristotle, and his expedition reflected that: cartographers, naturalists, and philosophers travelled with the army. Across his conquests he founded Greek-style cities (at least twenty 'Alexandrias'), and through them Greek language, art, architecture, and philosophy carried far beyond the Mediterranean.

After his death the empire was divided among his generals (the Wars of the Diadochi). But the successor Hellenistic kingdoms — Ptolemaic Egypt, the Seleucid realm in Anatolia and Syria, Antigonid Greece — sustained the cultural synthesis he had begun for centuries. Greek became the common tongue of the eastern Mediterranean, the Library of Alexandria rose, and mathematics and astronomy leapt forward. Alexander's enduring legacy lies in the lasting transformation of the lands he conquered: the very idea of a 'Hellenistic world' starts with him.