This is an anthology of poetry from Sumerian, the first language to be written, and the earliest extant literature. It contains most of the more important poetic texts, divided into eight categories: the texts concerning Dumuzi (the dying and resurrected shepherd god, similar to the later Adonis), including variations of his courtship and marriage to Inanna and his death; lovesongs, ostensibly about kings and queens, and very sexually explicit, as is much of the Sumerian poetry; three hymns addressed to Enlil, Inanna, and Nanshe respectively; myths, including the famous "Descent of Inanna" into the underworld; two Aratta epics and "Gilgamesh and Aka"; the "Cursing of Akkade"; three hymns to temples; and three laments for cities and temples destroyed in the barbarian conquest of Ur.
Not knowing Sumerian, I can't speak to the accuracy of the translations, but Jacobsen was considered a major expert. Not everything is understood, and there is room for much disagreement. The translations are fairly understandable, although the translator has a penchent for using the most archaic and obscure English vocabulary possible. He says in the introduction that he was planning a companion volume to include the prose works, but I haven't found any indication that it was ever published; Jacobsen died in 1993.