After Alexander had advanced far enough Darius III fled, and was eventually killed by a tribal chieftain. Alexander did not stop with the capture of the Persian empire but decided to press on into India. However, when his men saw the Indian War Elephants they refused to go any further, and threatened to mutiny if forced. From here Alexander and his army returned back home.
Under Alexander the Great's rule he established the city of Alexandria. The city contained The Great Library which allegedly had 500,000 books. Another feat was that the empire had been united in one form of Greek, known as Koine, or Common. Alexandria had scientists who studied anatomy, astronomy, and geology. After the Romans conquered the empire such practices faded away until the Renaissance Era.
The conquest and establishment of Alexander's empire was the greatest accomplishment ever seen in the ancient world. It is not entirely clear what vision he had for the future because he died at the young age of 33 in 323 BC from an illness. However, it appears as if his goal may have been to unite and globalize his empire. He forced his generals to take Persian wives, and he himself also took a Persian wife.
After his death the empire split into four kingdoms led by his generals. Because of the split the empire was again divided, and therefore not as strong as when it was united. Eventually Egypt again was under Pharaoh rule. Warring broke out among these kingdoms, leaving them in the same situation of the Greek city-states that predated Alexander's empire.