The Sumerian flood myth is part of a larger text often called the Eridu Genesis. The text is extant on a single tablet preserved from the Old Babylonian Period (1900-1600 BCE) that was found at Nippur. The Sumerian text is fragmented but still provides a good indication of the existence of the flood myth in Sumerian.
It was first published in 1913/14 by Arno Peobel but has been re-edited several times since. Below is a list of publications including the original publication of the text and multiple transliterations and translations.
Atrahasis is the name of the hero in the earliest independent flood narrative in Akkadian. The text was likely composed in Old Babylonian, highly influenced by - or even a translation of - a Sumerian precursor similar to the story in the Eridu Genesis. There are a number of tablets containing parts of the text in Old Babylonian and Neo-Assyrian as well as a few in other Akkadian dialects.
The earliest publication of parts of the text was in 1876 by George Smith, though he was working with fragmentary Neo Assyrian tablets and did not have a full understanding of the text. The Old Babylonian version was first made known by V. Scheil in 1898, but it was Heinrich Zimmern in 1900 who recognized that Smith and Scheil had published two versions of the same work.
The order and extent of the text were first understood in the 1950s when Jørgen Laessøe rearranged the extant fragments and produced a cohesive narrative. The fullest and to date most detailed publication of the story is the 1969 edition and translation by W.G. Lambert and A.R. Millard.