What are some possible research questions based on The Epic of Gilgamesh?

This
really depends on the level of the research. A scholar in a postgraduate program would be
reading the tablets in the original language and researching points of meaning or grammar or
perhaps comparing descriptions of objects in the epic with those found by archaeologists. An
undergraduate student in an introductory class might be reading the poem in English translation
and trying to prove to a professor that she had read the assigned text rather than making
original discoveries. 

If you are thinking about a topic for an undergraduate
research paper and reading Gilgamesh in translation, some possible topics
which require research outside the original text would be:

• Material Culture: Various different objects such as weapons are described in
  Gilgamesh. Look at museum websites and published excavation reports to
  compare some one class of objects or architectural features to the objects described in the
  epic. 
• Gilgamesh in Mesopotamian Art: Look at depictions of Gilgamesh in
  Mesopotamian art and discuss what they add to our impression of the epic.


• Related Stories: Choose one character from Gilgamesh, such as the
  goddess Ishtar, and look at how that character is portrayed in other works of the
  period. 
• Law Codes: Several early Mesopotamian law codes are preserved.
  Investigate how they can illuminate our understanding of Gilgamesh.
• Compare
  and contrast Gilgamesh with another work of Mesopotamian literature or a
  work of a related culture such as the Bible or Hesiod's
  Theogony. 
• Investigate how
  Gilgamesh may be metaphorically addressing the issue of deforestation in
  the ancient world.