Baugi is attested to in Skáldskaparmál in Snorri's Prose Edda, and does not appear in other texts. Due to his absence in other relevant mythological texts, numerous scholars have argued that Baugi either comes from a source that is not extant today or was an invention of Snorri's, accidental or intentional.
In Skáldskaparmál, Odin worked for Baugi while in disguise in an effort to obtain the mead of poetry, which was possessed by Suttungr at the time. Odin arranged for the death of nine of Baugi's slaves unbeknownst to Baugi, and then offered to do their labor in exchange for a single drink of the mead of poetry.
Odin then spent the night at Baugi's place. Baugi complained that business did not go well since his slaves had killed each other and he could not get anybody to stand in for them. Odin, who said his name was Bölverk, proposed to do their work in exchange for a draught of Suttung's mead. Baugi agreed, saying that he would try to persuade his brother. During summer, Bölverk did the work as agreed and, in winter, asked Baugi for his owing. They both went to Suttungr's, who refused to give a single drop of the beverage.
Bölverk then suggested Baugi to use a trick. He gave him the drill Rati and asked him to dig into Hnitbjörg mountain. After Baugi tried to deceive him, a hole was actually dug and Bölverk slipped into it, having taken the form of a snake. Baugi tried in vain to hit him with the drill.
He arrived by Gunnlöd, with whom he spent three nights. Thus he could have three draughts of mead. But each emptied a container. He then transformed into an eagle and flew away. When Suttungr discovered the theft, he took the shape of an eagle and pursued Odin. When the Æsir saw him, they displaced containers in which he spat his loot out. But Suttungr was so close to him that he let some drop backwards. Anybody could drink this part, which is known as the "rhymester's share" (skáldfífla hlutr).
But the mead of poetry was given by Odin to the gods and to the men gifted in poetry.