Alexandria got its name from Alexander the Great, who, obviously, named it after himself! Upon his death, he was buried in the city bearing his name. After being dubbed and named by Alexander, it was soon the greatest city in Egypt. It held the largest library filled with rare scrolls and texts. It certainly rivaled any library known to the Greeks and Roman's holding almost 500,000 volumes. One of the seven wonders of the ancient world, the Lighthouse of Pharos, was located in Alexandria. Many philosophers came to Alexandria to study and debate.
Unfortunately, the Great Library was burnt to the ground in 48 BC as Julius Caesar pursuing the pharaoh, Pompey, into Egypt. He ordered that only the ship be set on fire, but the fire grew out of control until it consumed the city.
Regardless of Roman intentions, it was under the control of the Egyptians until 31BC, when it fell under the control of Roman's, led by Augustus. And it wasn't just the constant fights with Rome that Alexandria had to worry about, but also the internal wars between the Jews, Christians, and pagans all living within the same quarters. They started many a riot between each other, massacring one another in the streets.