In Norse mythology, Fornjót (Old Norse: Fornjótr) was an ancient giant and king of "Gotland, Kænland and Finnland" meaning Gotland, Kvenland and Finland Proper. His children are Ægir (the ruler of the sea), Logi (fire giant) and Kári (god of wind).
The name has often been interpreted as forn-jótr "ancient giant", and Karl Simrock (1869) because of this identified Fornjotr with the primeval giant Ymir. But it is also possible, as was suggested by Peter Erasmus Müller (1818), that it is one of a well-established group of names or titles of gods in -njótr "user, owner, possessor", which would make Fornjótr the "original owner" (primus occupans vel utens) of Norway.
Logi appears by that name in Gylfaginning in the tale of Thor and Loki's journey to the castle of the giant Útgarða-Loki in Jötunheimr where Loki was pitted against Logi in an eating contest. The contestants appeared to be equal in speed at eating meat from the bone, but Logi also consumed the bones and even the wooden trencher in which the meat was placed. Útgarða-Loki afterwards explained that Logi was really fire itself.
In the Saga of Thorstein Víking's son
The beginning of Þorsteins saga Víkingssonar ('Saga of Thorstein son of Víking') brings in a king named Logi who ruled the country north of Norway. Logi was the handsomest of men, but with the strength and size of the giants from whom he was descended. (Logi's ancestry is here not otherwise specified.) Because Logi was larger and stronger than any other man in land, his name was lengthened from Logi to Hálogi ('High-Logi') and from that name the country was called Hálogaland 'Hálogi's-land' (modern Hålogaland or Halogaland).
The saga tells that Hálogi's wife was Glöd (Glǫð 'glad'), the daughter of Grím (Grímr) of Grímsgard (Grímsgarðr) in Jötunheim in the far north and her mother was Alvör (Alvǫr) the sister of King Álf the Old ('Álfr hinn gamli') of Álfheim. Or perhaps, the name of Hálogi's wife should be rendered instead as Glód (Glóð 'red-hot embers') if this Logi is indeed either identical or confused with Logi as a personification of fire. The names of his daughters in this account were Eisa 'glowing embers' and Eimyrja 'embers', the fairest women in the land, whose names were later applied to the things which became their meaning, certain indication of the original fiery nature of their father. (Wife and daughters are sometimes wrongly ascribed to Loki rather than Logi in secondary sources.)
Two of Hálogi's jarls named Véseti and Vífil (Vífill) abducted Hálogi's daughters and fled the country. At that point Hálogi is out of the story. Véseti settled in Borgundarhólm (Bornholm) where Eisa bore him two sons named Búi and Sigurd Cape (Sigurðr Kápa). Vífil fled farther east to an island named Vífilsey 'Vífil's Isle' where Eimyrja bore him a son named Víking (Víkingr) who was father of Thorstein (Þorsteinn) the hero of the saga. Víking is made out to be a contemporary of a King Ólaf (Ólafr) who is said to be the brother of King Önund (Ǫnundr) of Sweden. Descendants of Thorstein appear in Fridthjófs saga ins frækna (Friðþjófs saga ins frækna 'Saga of Fridthjof the Bold') and in the Starkad section of Gautreks saga 'Gautrek's saga'.
This account cannot be reconiciled with the account in the Hversu and Orkneyinga saga without assuming multiple figures with the same names. In Thorsteins saga Víkingssonar, Logi (a descendant of giants) is the husband to a niece of King Álf the Old of Álfheim who himself is the husband of Bergdís the daughter of King Raum (Raumr) of Raumaríki. In the other accounts Logi is the brother of Kári who is a distant ancestor of Raum the Old who is father of Álf or Finnálf (Finnálfr), king of Álfheim.