What are three ways in which Alexander the Great influenced the rest of the world?

Alexander's conquests facilitated the spread of Greek culture. Territories such as Egypt were thoroughly Hellenized, becoming important centers for the study and dissemination of Greek learning. The world-famous Library of Alexandria—a city named after Alexander—was one such center, attracting scholars from across the known world. The ruling dynasty of Egypt during the Hellenic period, the Ptolemies, were themselves Greek-speaking and immured in Greek culture. The founder of the dynasty, Ptolemy, was not an Egyptian, but the son of a Macedonian noble. The last ruler of the Ptolemaic dynasty was arguably the most famous of all—Cleopatra.
Under life in the traditional Greek city—or polis—there was no real distinction between public and private lives. In devoting one's life to the city-state, a citizen was also acting in his own best interests. In the Hellenistic world, however, a degree of individualism gradually began to emerge. In due course, the polis was replaced by the world of the cosmopolis, a huge city consisting of many different cultures and ethnic identities. In such a large urban environment, citizens became separated from the state. As such, people tended to pursue their own individual interests. In the Hellenistic world, unlike the world of Classical Greece, the state was remote, bureaucratic, and alienated from its citizens.
In the Hellenistic world, a Greek dialect emerged called koine. This developed into the common language of the Empire, the lingua franca of the Mediterranean world for centuries. Koine was especially influential in helping to facilitate the spread of the Christian message, and it's notable that the New Testament was written in this particular dialect.