For a person who enjoy Norwegian literature (and in some cases also Norwegian history), there are a few Norwegian authors that should be familiar. If you know at least most of these, you have made a good start.
Aasmund O. Vinje (1818–1870)
Agnar Mykle (1915–1994)
Alexander Kielland (1849–1906)
Alf Prøysen (1914–1970)
Amalie Skram (1846–1905)
André Bjerke (1918–1985)
Andreas Munch (1811–1884)
Anne Holt
Anne Karin Elstad (1938–2012)
Anne-Cath. Vestly
Arild Nyquist (1937–2004)
Arne Garborg (1851–1924)
Arnulf Øverland (1889–1968)
Bjørnstjerne Bjørnson (1832–1910)
Camilla Collett (1813–1895)
Dorothe Engelbretsdatter (1634–1716)
Erlend Loe
Gunnar Staalesen
Hans Henrik Thaulow (1754-1823)
Henrik Ibsen (1828–1906)
Henrik Wergeland (1808–1845)
Herbjørg Wassmo (1942–)
Hulda Garborg (1862–1934)
Inger Hagerup (1905–1985)
Ingvar Ambjørnsen
Ivar Aasen (1813–1896)
Jens Bjørneboe (1920–1976)
Johan Falkberget (1879–1967)
Johan Herman Wessel (1742–1785)
Johan Nordahl Brun
Johan Sebastian Welhaven (1807–1873)
Jon Michelet (1944–2018)
Jonas Lie (1833–1908)
Jørgen Moe (1813–1882)
Jostein Gaarder
Kjell Aukrust (1920-2002)
Knut Faldbakken
Knut Hamsun (1859–1952)
Kolbein Falkeid
Lars Saabye Christensen
Linn Ullmann
Ludvig Holberg (1684–1754)
Nils Collett Vogt (1864–1937)
Nordahl Grieg (1902–1943)
Olav Aukrust (1883–1929)
Olav H. Hauge
Oskar Braaten (1881–1939)
Per Sivle (1857–1904)
Peter Christen Asbjørnsen (1812–1885)
Petter Dass (1647–1707)
Sigbjørn Obstfelder
Sigrid Undset (1882–1949)
Siri Pettersen
Siri Økland
Thorbjørn Egner (1912–1990)
Unni Lindell
Vigdis Hjorth