Evidence shows that a group of Irish Monks called the Papar inhabited Iceland after travelling to seek colitude. It is believed they left around the time or just after the Norsemen arrived

Naddodd discovered Iceland in 861 whilst sailing from Norway to his new home in the Faroe Islands when his boat travelled off course. A Swedish Sailor also accidentally landed on Iceland and stayed the winter
The first Norwegian settlement on Iceland was established by a Chieftain Ingolfur Anarson around 874.
Many other Norse chieftains began to settle with their families and slaves over the following decades.
In 930 the ruling chieftans establishes the Alpingi assembly, which acted as a democratic parliament.
The settlers predominantly worshipped the Norse gods. However, in the 10th century political pressure from Europe increased and many of the Icelanders accepted Christianity as their faith.
In 1000 as civil war between religious groups seemed iminant, an elected chieftan decided that the country should convert to Christianity, whilst Pagans would be allowed to worship privately
In in the 1200s, the Sturlungar family clan waged war on the other clans in Iceland, the chieftains accepted their sovereignty around 1263 and the Norwegian Monarchy was nationally accepted.
In 1297 wealth and power moved from aristocracy to the church.

In 1380, as part of the Norwegian Kingdom, Iceland became part of the Kalmar Union. A union that united Denmark, Norway and Sweden under one Monarch
1400s, Iceland declind due to disease and famine
In 1602 Denmark implemented foreign trade so Icelanders could only trade with Danish merchants
Smallpox hit Iceland from 1707-1709 killing around 30% of the population
Then in 1783 the Laki Volcano erupted causing the death of about 20% of the population
The Icelandic parliment (Alpingi) was abolised by the Danes in 1800 and then re-established in 1843
Denmark granted Iceland a constityation and some home rule in 1874
Iceland became a sovereign state in 1918, still in union with Denmark
The Republic of Iceland was formed in 1944 as the country was officially declared as independent from Denmark