humanity as a whole.

Enkindu is the man-beast who becomes Gilgamesh's best friend. Found in the wild, he represents mankind's origins as uncivilized beasts. He eventually comes into society and learns to be truly human by gaining community—particularly with Gilgamesh. The two end up working together to find the secret to immortality, which is the existential goal of humanity. During all of this, Gilgamesh's city becomes a renowned civilization of which he is the king, showing the ascent of humanity through its pursuits.

Society is presented as an interesting force in The Epic of Gilgamesh. It is a rather traditional society, with men and women handling different roles. Gilgamesh himself rules over the ancient Sumerian city Uruk, which is the main social and cultural setting of the story.

However, society is not represented as perfect. Gilgamesh is initially a corrupt figure who bullies his subjects into doing whatever he wants them to, whether it's fighting him or sleeping with him. Though society has rules, those in power are free to trespass them.

Society is contrasted with nature, represented by the wild man Enkidu. He initially shuns society, living with the animals, until he is "civilized" by an extended sexual encounter with a woman. Then he becomes a social being and eventually Gilgamesh's dearest friend. He challenges Gilgamesh's bullying and ultimately helps him grow into a better person.

So, society is a double-edged sword in Gilgamesh: it can corrupt as well as enlighten and ennoble.

The question hinges on what you mean by “society.” I’ve always thought that the figure of Gilgamesh represents a kind of transition in the way ancient societies are understood. That is, Gilgamesh is a figure who clearly has mythological origins—he is part god, a heritage that makes him incredibly strong and wise. His rule over Uruk is more than by “divine right”—he actually is divine! There is a sense in which his conflict with Ishtar supersedes his role as king, or, rather, that his killing the bull and defeating Enkidu are somehow evidence of his kingly capabilities. What makes Gilgamesh so compelling, however, is his humanity, his friendship with Enkidu, and his quest for immortality after Enkidu’s death. His decision to take Utnapishtim’s advice and return to rule Uruk as a mortal suggests that society is not intertwined with the gods, but is, in fact, a fully human development, and made all the stronger for that.

Although many elements of the Epic of Gilgamesh are mythical or fictional, the protagonist Gilgamesh was an historical king of Uruk whose rulership is attested by ancient king lists. Many aspects of the epic are consistent with information obtained from archaeological and other non-literary sources. 

The epic represents the society of Uruk as one in which the monarch has absolute power. Even when subjects disapprove of his actions or he acts in a manner that violates social norms, there is no mechanism by which ordinary people can prevent him from doing as he pleases. 

Religion is an important element in Gilgamesh's society, which is ordered as a theocracy, with there being no clear distinction between secular and religious authority. The portrait of the constant intervention of the gods in human affairs reflects the actual importance of temples in the administration of Uruk.

The society is represented as having very distinct gender roles and strong social stratification. The society is extremely hierarchical. As well as class distinctions, the society is highly urbanized with a strong division between city and countryside. The society is also strongly militaristic, and in a constant state of potential conflict with neighboring kingdoms.