This article is from the Nordic countries FAQ, by Antti Lahelma and Johan Olofsson, with numerous contributions by others.
Greenland is said to have been discovered by a man called Gunnbjörn whose
ship had gone off course. It was, however, Eiríkr Þorvaldsson (a.k.a Eric
the Red) who explored and named the island, and ruled the first colony of
settlers. He who was born in Norway in the mid-10th century, but went to
Iceland as a child after his father was banished from Norway. A violent man
as he was, Eiríkr himself was banished from Iceland, and set forth on an
expedition westward from Iceland. In 981 he got to Greenland (a name he gave
to encourage settlers to go there), and spent the next three years exploring
it. After that he returned to Iceland and led an expedition of 25 ships to
settle (c.985) in southwestern Greenland. This settlement survived until the
late 15th century. Eiríkr himself settled at Brattahlið (Tunigdliarfik) in
Greenland, where he died sometime after the year 1000.
The most important written sources recounting the discovery and settlement
of Greenland are Ari Þorgilsson's Íslendingabók and Landámabók. There are
also two colourful sagas, Grænlendinga Saga (The Saga of the Greenlanders)
and Eiríks saga rauða (The Saga of Eric the Red), but these were composed
only in the early 13th century and are often fanciful and contradict each
other in places.
Greenland's attraction was that it had better pasture for sheep, goats and
cows than Iceland, where the soil had already become poor after about a
century of heavy exploitation. Farmers had never lived there, the climate
was probably a bit milder than today, and some of the fertile lowlands which
now have have disappeared under sea were above surface at that time. There
was probably also quite a lot of driftwood in Greenland at that time. Catch
was plenty in the sea, and there were reindeer, bears and birds to hunt on
land. Pelts of polar bears and arctic foxes, whalebone and walrus tusks were
used to pay for the essential imports, such as metal, timber and grain, as
well as luxury goods. But the colony was vulnerable if there were epidemics
among animals or people or even small climactic changes, and it died out
sometime in the 15th century -- the exact reason isn't known. In 1712,
centuries after the links between Greenland and the rest of the world had
been broken, the king of Denmark-Norway sent an expedition to Greenland with
pastor Hans Egede to nurture the Christian faith among the Viking
descendants, but none had survived. The Eskimos had long since penetrated to
the southernmost point of the country, and these were the Greenlanders Egede
met.
 
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