Alexander, known as the Great Greek, was not Greek. He was a prince in the county of Macedonia. Macedonia was an empire located to the north of Greece.
Alexander had many teachers, one of which was Aristotle. Aristotle is another famous person that many refer to as an ancient Greek. But Aristotle was also born in Macedonia. Aristotle lived in Greece for a really long time, though. He loved the Greeks. He believed in the Greek gods. He knew Greek history and the Greek language and Greek theatre. Aristotle thought the Greeks were clever and interesting and talented, and he spoke of his admiration for the Greeks many times to his student, the young prince, Alexander.
Alexander grew up dreaming of the day he would be king. When he was king, he too would teach everyone about the Greek culture he had come to know and love so well. Obviously, Aristotle had a great effect on Alexander and what he believed.
But Alexander had other teachers, teachers that taught him how to wage war and how to conquer other people. His teachers tried to teach him that a Macedonian king was not merciful. But Alexander disagreed. He allowed every culture he conquered when he became king the opportunity to rule themselves. All he asked was that they be loyal to Alexander. And, he taught all the people he conquered all about the ancient Greeks - their stories, their myths, their gods, their language - everything, just as he had been taught.
Alexander never lost a battle, never, not even one. By the time he was 32, he had conquered the entire Mediterranean region, and even reached into the Indus River region. He probably would have kept going, but one day, he became ill and died. He was only 32 years old.
We owe Alexander a great deal. It was Alexander who spread the Greek culture throughout the Mediterranean. Without Alexander, that culture might not have survived. The Macedonians conquered the Greek city-states. The ancient Romans conquered the Greek city-states. Who knows what might have been lost without the teachings of Alexander the Great.