From the Wikipedia page 
Reykjavík Municipal Archives (Icelandic: Borgarskjalasafn Reykjavíkur) is an independent institution of Reykjavík municipality, the most populous municipality and capital of Iceland. The Reykjavík Municipal Archives collects, records and preserves various records pertaining the operation and history of both public institutions as well as private enterprises and individuals related to Reykjavík.
The Reykjavík Municipal Archives was originally established in 1954. Before that city records were kept at the National Archives of Iceland.
The website is .