In the Epic of Gilgamesh, the surviving tablets were recorded in cuneiform.
Cuneiform is a writing system made by pressing the end of a reed stylus into wet clay. The resulting wedge-shaped marks gave the system its modern name, from a Latin term meaning wedge-shaped. Mesopotamian scribes used it for several languages, including Sumerian and Akkadian.
The Epic of Gilgamesh survives in multiple versions and fragments written on clay tablets. The best-known long version is the Standard Babylonian edition, written in Akkadian using the cuneiform script. Earlier Sumerian poems about Gilgamesh also survive in cuneiform, but they are separate compositions rather than one continuous edition.
Cuneiform was not an alphabet. Its signs could represent words, syllables or grammatical elements depending on context. That flexibility allowed scribes to use it across centuries, languages and genres.