The old name of Trani was or Tirenum. An old myth says that Tirenus built the city. Tirenus was the son of Diomedes, a hero in ancient Greece who fought in the Trojan War. The city was on an ancient Roman map called the "". It was the first map to show this city. The map was made in the 3rd century. At first, Trani was a very small city and not very important. It started to grow and be more important in the 9th century. At that time, the Lombards (a Germanic people) ruled Trani. Later, the Byzantine Empire ruled the city.