Bárður saga Snæfellsáss is a relatively late “Íslendingasaga”, probably dating to the early 14th century. The saga falls into two sections that were distinguished in the early 18th century and are probably written by different authors.
In section 1, the main character is Bárður Snæfellsáss.
Bárður's mother was human, but his father was half risi (giant) and half troll and he was fostered by Dofri, the "mountain-dweller" of Dovrefjell. By his first wife, Dofri's daughter Flaumgerðr (who also had a human mother), Bárður had three tall, beautiful daughters: Helga, Þordís and Guðrún. By his second wife, Herþrúðr, who was human, he had six more daughters.
Bárður, his wife and his daughters emigrated to Iceland and came ashore at a lagoon on the south shore of Snæfellsnes which they named Djúpalón; he built himself a farm which he called Laugarbrekka. Þorkell, Bárður's half-brother from his mother's second marriage to a jötunn, lived at Arnarstapi and had two sons, Rauðfeldr (Red-cloak) and Sölvi. The sons of Þorkell and the daughters of Bárður used to play together. One day, when there was pack ice along the shore, Rauðfeldr pushed Helga out to sea on an iceberg. She drifted unharmed to Greenland and there found a lover, but Bárður was infuriated. He pushed Rauðfeldr into the Rauðfeldsgjá ravine and threw Sölvi off Sölvahamar, a high cliff on the coast east of Arnarstapi. Bárður and Þorkell fought and Þorkell's leg was broken; he moved out of the district.
After these events, Barður gave away his land and vanished into the Snæfellsjökull ice cap. He became known as Bárður Snæfellsáss, meaning the "guardian spirit" of Snæfell, because "they practically worshipped him on the peninsula and called upon him in times of difficulty. For many he also proved to be a source of real help in need". He wandered the region "in a grey cowl with a walrus-hide rope around him, and a cleft staff in his hand with a long and thick gaff," which he used when walking on glaciers. He brought Helga back from Greenland, but she pined for her lover and could not stand to stay with her father. When called on, he rowed out alone to save Ingjald of Ingjaldshvoll, who had been lured to a dangerous fishing spot by a troll-woman and kept there by a mysterious fellow fisherman who called himself Grímr and whom people thought "must have been Thor." He and Þorkell are said to have made peace and lived together for a while.