Logi (Old Norse: "fire") is a jotun (giant) in Norse mythology, a deity and personification of fire. Logi is the son of Fornjot, thus brother of Aegir (god of the sea) and Kári (god of the wind).
In the Þorsteins saga Víkingssonar, ch. 1, mention is made of a king Logi or Hálogi, who reigned over the northern lands of Norway, married to Glóð with whom he had two very beautiful daughters, Eisa and Eimyrja. Eimyrja married a warrior named Vífil and they had a son named Viking, the protagonist of Þorsteins saga Víkingssonar.
Logi has sometimes been confused with Loki, another Norse deity.
Hálogi according to Þorsteins saga Víkingssonar is the first king that Hålogaland, Norway had at the beginning of the 10th century and to whom the region owes its name. At first he was called Logi, he was a descendant of jotuns, bigger and stronger than any other human being and was therefore nicknamed Hálogi (great Logi).
Hálogi married Glöd (Glǫð), daughter of Grím (Grímr) of Grímsgard (Grímsgarðr) in Jotunheim, a place in the far north. Glöd's mother was Alvör, sister of King Alf the Elder ('Álfr hinn gamli') of Alvheim. From their union were born two daughters, Eisa and Eimyrja, the most beautiful women in the kingdom.
Two jarls of Hálogi named Véseti and Vífil (Vífill) sought the hand of the king's daughters but were rejected and then abducted and eloped with the princesses. Véseti settled with Eisa on the island of Borgundarhólm where they had success and offspring, two sons Búi and Sigurd Kappe (Sigurðr Kápa). Vífil escaped far to the east, to another island called Vífilsey (Vífil's island) where Eimyrja had a son named Víkingo (Víkingr) who in turn would father Thorstein (Þorsteinn), hero of the saga.