What is the main theme of The Epic of Gilgamesh, and what is the historical background of Gilgamesh? Is it a believable story?

The
historical figure Gilgamesh, if he existed as many scholars believe, was a Sumerian king who is
thought to have ruled over the city of Uruk circa 2800-2500 B.C. (in modern-day Iraq).

 is incomplete.  Fragments of tablets of the epic date from 2100
B.C., and what is widely read today is a nineteenth-century translation.

The
epic contains many themes consistent with man's journey through life; it could be said that the
earliest tablets are concerned with man's desire for power and how he faces limitations imposed
by the gods.  The relationship of Gilgamesh and Enkidu could be seen in psychological terms as
the struggle between the id and the ego.  Many of the epic's stories correlate with biblical
stories (i.e. the deluge) and are also reminiscent of episodes from Homer's The
Iliad  and The Odyssey.  

The overarching
theme of the epic centers on man's rejection of his mortality and his consequent desire for
immortality.  Since life as man knows it is not eternal, if he wishes to be remembered, it must
be for kindness and love, not the attainment of the power to oppress others.

To answer the last part of your question, if one reads the epic's episodes as
metaphors, it is "believable."  The acquisition of wisdom and acceptance of one's
humanity are lessons that apply to us all, even if some of the trappings of the stories
challenge our credulity.