Why is Gilgamesh still relevant?

This great epic's relevance lies chiefly in the fact that it presents us with a recognizable portrait of an individual's moral growth. When the poem begins, Gilgamesh is lord and master of all he surveys, a crazed, psychopathic tyrant who believes he can do as he pleases. However, over the course of the poem, he develops into a wiser, more mature king, as he comes to realize that brute strength isn't everything.
As he prepares himself for battle with the fearsome Humbaba, Gilgamesh has the courage to look deep inside his soul and confront his own demons. And while most of us in our lives won't actually get to engage in mortal combat with monstrous, forest-dwelling giants—thank goodness!—we will at some point have to confront our innermost fears, whatever they are. That being the case, we can do a lot worse than look to the great Gilgamesh as an example of how to overcome the many fears that so often hold us back in life. In the moral example presented to us by Gilgamesh lies the epic's enduring relevance.

The Epic of Gilgamesh is one of the first written literary works in history and the first complete epic that has been discovered. Not only does it illustrate the culture, mythology, and history of ancient Sumeria, but it is one of the earliest surviving works of great literature from any culture. On an archaeological and literary level, studying Gilgamesh offers more insight into the development of written literature as we know it.
It also exemplifies the similarities in interests and values between the ancient Sumerians and modern people. Ultimately, Gilgamesh's journey to find the secret to eternal life and his grief over losing Enkidu portrays the fear and uncertainty every person has when facing death. Just as people create art to grapple with life's major questions today, the ancient Sumerians may have created the epic to deal with feelings of grief and fear surrounding death and explain what they thought the afterlife looks like. This is relevant because, in many ways, artists do the same thing today: respond to the painful or mysterious events in life with work that seeks to explain or validate it.