Norway actually has three official written languages bokmål (book-tounge, sic!), nynorsk (Neo-Norwegian) and Sami (spoken by the lapps) The two first are not very far apart, but have slightly differt rules of grammar and vocabulary. To put it simple bokmål (which is the chosen language by 90%) resembles Danish and Nynorsk is closer to oral language and also to archaic Norwegian and (hence) Icelandic. Languages has been (and still is to some extent) a source of a great many arguments up here.
Sami is (as far as I know) related to Finnish, and not spoken (or understood) by the majority of Norwegians. The Lapps are an ethnic group found in the north of Norway and Sweden as well Finland. Still as far as I know, they intercommunicate quite easy between groups from different countries. Furthermore, with the exception of very old people, lapps are bilingual.