One of the things that makes Iceland unique in Europe is the fact that Icelanders know the year the first settler, Ingólfur Arnarson, came to Iceland from Norway. The Icelandic script, Íslendingabók (Book of Icelanders), written by Ari the wise, tells of the first men coming to Iceland on explorations.
Three expeditions came to Iceland, but the first men who came to Iceland to live there permanently were Ingólfur and Hjörleifur. The two came to Iceland in 874. Hjörleifur was killed by his slaves, which only left Ingólfur and his wife Hallgerdur Fródadóttir. They settled in Reykjavík, now the capital of Iceland. An excavation in the center of Reykjavík seems to indicate that this story might be true. It shows that the remnants of building stem from the year 871+/-2 years. That website is worth examining. It has a number of interactive features and recreates the 871 environment.
In recent years some archeologists have begun to doubt that the first year of settlement was really around 870. Those who subscribe to this view point to a number of finds, but most of those actually stem from the years after 870 A.D. However, they bring interesting new facts to live.
RÚV tells us of archeologist Bjarni F. Einarsson, who last year studied a settlement building near the church at Kirkjuvogur in Hafnir on the Reykjanes peninsula (close to Keflavík). Einarsson says the building was probably not a farm. It could not have been built later than 880 A.D. The building contains a lot of rocks, but such buildings have only been found in the Westmann Isles and in Papey Island in the east of Iceland. The fact that no other buildings are close to the one found show that it is not a farm.
Einarson points out that it is known that people came to Iceland before the country was settled. Íslendingabók actually says that Irish monks were in Iceland before the Nordic settlers came. They were called Papar, and Papey draws its name from these Irish monks that left behind bells and crosiers.