The main idea of this story that traces Gilgamesh's development as a king and a leader of his civilization is that it is always possible for people to change.
This applies even to Gilgamesh, who is presented in Bryson's retelling of the epic Babylonian poem as something of a monster, a brutal, ruthless tyrant almost out of control.
Right at the start of Bryson's retelling, we see a group of elders from the city of Uruk complaining to the gods about the crazed, almost psychotic behavior of their tyrant king. At first, the father of the gods, Anu, is unsympathetic to their desperate pleas. But eventually, he relents and sends down Enkidu, a creature in manlike form who will tame Gilgamesh, making him more human. And that's precisely what Gilgamesh becomes in due course, thanks to the extraordinary friendship that develops between himself and Enkidu.
At first, it didn't seem possible that Gilgamesh was capable of change. But in due course, as a result of his many experiences and adventures, he becomes a wise and courageous man, someone completely different from the brutal tyrant he was at the beginning of the story.