Tribal Occupation Celts (800-874) Foreign Rule Norway (874-930) Republic of Iceland Legislature -Althing (930-1262) Foreign Rule Norway (1262-1380) Denmark (1380-1944) Republic of Iceland Presidency -Sveinn Bjornsson (1944-1952) -Asgeir Asgeirsson (1952-1968) -Kristjan Eldjarn (1968-1980) -Vigdis Finnbogadottir (1980-1996) -Olafur Ragnur Grimsson (1996- )