On Flatey Book, Red Eric Saga and the whole bibliography for the Vinland voyages, including that of Thorfinn, see Leif Ericsson and Vinland.
The less trustworthy history of the Flatey Book makes Biarni Heriulfsson in 985 discover Helluland (Labrador?) as well as other western lands which he does not explore, not even permitting his men to land; while Leif Ericsson follows up Biarni's discoveries, begins the exploration of Helluland, Markland and Vinland, and realizes some of the charms of the last named, where he winters.
Here they found the "self-sown" wheatfields and vines of Leif's Vinland, and here accordingly they settled and built their huts above the lake (1004-1005).
Later, in 1003, an Icelander, Thorfinn Karlsefni, who was visiting the Greenland colony, and who had married Gudrid, the widow of Leif's brother Thorstein, set out with four vessels and 160 followers to found a colony in the new lands.
The only important phase of the Vinland voyages that has not been definitely settled is the identifications of the regions visited by Leif and Thorfinn.
