Iceland was settled by rough, independent personalities primarily from Norway/Sweden, but there are records of people from other parts of Scandinavia, the British Isles, Faroe Islands, and Russia. They left their home country to settle Iceland from 874 AD - 930 AD for a variety of reasons:
1. Arable land was becoming scarce. Traditionally, the oldest son inherited part of the parents' farm and the other sons had to move away and buy their own land or become a professional blacksmith, cobbler, clergyman, etc. If that didn't suit them, I guess some moved to Iceland. After a few generations, the farm portions weren't large enough to sustain the oldest son's family and some of them moved to Iceland.
2. Outlaw types and people who were banished from their hometowns as punishment went to Iceland to escape ridicule and find a fresh start.
3. Escape the current king, Harald Fair-hair.
These Norsemen were excellent boat builders and sea farers. Families moving to Iceland forged across raging oceans in small, shallow boats with their tools, provisions, and domestic animals.
(a replica of a very nice, large, Norse ship)
If they made it, they then set about exploring, claiming land, building homes, sowing seed and raising livestock. There were no large native land animals to hunt, but there was an abundance of fish and migrating fowl to catch and preserve for the winter. Though the northern side of the island is within the arctic circle, the southern side of the island has areas of fertile farm land and is relatively warm and mild due to the Gulf current bringing warm air and water north from the Caribbean area.
(an example of some early settlers)
An amazing aspect about the new colony on Iceland was that despite the inhabitants' varied backgrounds, they created their own democratic parliament and maintained an orderly, non-centralized society. Within about 50 years from the first record of voyages to Iceland, the Icelandic Parliament (Alþingi, or Althingi) was established (in year 930 AD). It is claimed to be the longest standing democratic parliament - from 930 AD to present day - because even after Iceland accepted Norwegian rule in 1262 and Danish rule from 1814-1944, their geographic distance allowed the Althingi to more or less continue.
The island was divided into 4 regional quarters (eventually a 5th was added to make 5 "quarters") made of clans called goðorð (sounds like"go-thorth"). The clan leaders were called goði (sounds like "go-thee") and they provided protection and appointed judges to settle disputes within the goðorð.
There was a single, elected lawspeaker, or lögsögumaður, who memorized the lawbook and would recite it orally once a year to the gathered goði at the Alþingi. Occasionally, a conflict would arise crossing regional borders, and the representatives would seek the lawspeaker's advice. The current lawspeaker is Ásta Ragnheiður Jóhannesdóttir.
The Alþingi/Althing met near present day Reykjavik at Þingvellir, or the Parliamentary plains (sounds like "thing-vet-leer"), an area large and flat enough (see photo above) to make camping and tending animals convenient for the attending goði and their household for the duration of the Alþingi session (up to a few weeks).
The lawspeaker stood on a large rocky area called the Lögberg, or Law Rock, in front of a natural amphitheater created by the separating North American and European tectonic plates.
The Alþingi moved from Þingvellir to Reykjavik in 1844.
Here are some poor quality photos I took of the building:
Denmark officially owned Iceland from 1814-1944. However, in 1940, when Denmark was occupied by Germany, Iceland became unofficially an independent state. In 1944, the Republic of Iceland was officially formed. The President of Iceland is the head of state and appoints the Prime Minister of Iceland, who is the head of government. Vigdís Finnbogadóttir, the 4th President of Iceland (from 1980-1996) was the World's first democratically elected female head of state. The current president is Ólafur Ragnar Grímsson (photo below in Springville, UT, 2005)
and the current Prime Minister is Jóhanna Sigurðardóttir