Reykjavík is the capital and largest city in Iceland.

Its latitude, at 64°08´ N, makes it the world´s northernmost capital of a sovereign state. It is located in southwestern Iceland, on the southern shore of Faxaflói Bay. With a population of around 120,000 (and over 200,000 in the Greater Reykjavík Area), it is the heart of Iceland´s economic andgovernmental activity.

Reykjavík is believed to be the location of the first permanent settlement in Iceland, which Ingólfur Arnarson is said to have established around 870 C.E. Until the 18th century, there was no urban development in the city location. The city was founded in 1786 as an official trading town and grew steadily over the next decades, as it transformed into a regional and later national centre of commerce, population, and governmental activities.

The first permanent settlement in Iceland by Norsemen is believed to have been established in Reykjavík by Ingólfur Arnarson around 870 AD; this is described in Landnámabók, or the Book of Settlement. Ingólfur Arnarson is said to have decided the location of his settlement using a traditional Viking method, by casting his high seat pillars (Öndvegissúlur) into the ocean when he saw the coastline, then settled where the pillars came to shore. Steam from hot springs in the region is said to have inspired Reykjavík´s name, which loosely translates to Smoke Cove (the city is often referred to as the Bay of Smokes or Bay of Smoke) The original name was Reykjarvík with an additional "r" that vanished around 1300.

Source: See here