The best place to make sense of how a sparsely populated volcanic rock in the North Atlantic ended up with sagas, parliaments, and Lutheran pastors. The permanent exhibition — "Making of a Nation" — runs from settlement around 870 to the present, with around two thousand objects: a Viking sword pulled out of a bog, a thirteenth-century church door carved with a battle scene, fishing implements, costume, and twentieth-century pop ephemera.
It is genuinely well laid out and not enormous; two hours is enough. Right next door is the Árni Magnússon Institute for the original saga manuscripts.