A couple of modern classics that you can pick up translated to English at a good Amazon website near you.
Jón Gnarr – The Pirate
In this second volume of comedian and former mayor of Reykjavík Jón Gnarr’s bleakly hysterical autobiographical writing, the scene is set for Reykjavík in the early eighties. At the outset, Jón is still in school, struggling under an education system with no concept of things such as dyslexia and ADHD, with most of his teachers simply assuming that he is—in the parlance of the time—retarded. After several unsuccessful forays into the job market, he finally finds his place among the young punks of Hlemmur, the Reykjavík transit station and legendary gathering place for the city’s derelicts and outcast kids (until its recent reopening as a gourmet food hall, that is). There, he discovers bands like Crass and Discard and finds solace in the anarchistic writings of Prince Kropotkin. Despite the book’s humorous narration, it also contains an undertone of fury against the faceless systems of society.
Sjón – The Whispering Muse
Valdimar Haraldsson, a peevish elderly academic obsessed with the connection between the obvious superiority of the Nordic race and a heavy pescetarian diet, is invited by a benefactor to partake in a cruise on the Black Sea with the Danish merchant vessel MS Elisabet Jung-Olsen. On board, he is introduced to the ship’s misfit crew, including the first mate Caeneus, who, it turns out, was one of the famed Argonauts, in search of the Golden Fleece. Night after night, the first mate regales the crew with his tales of the voyage and his later adventures. However, it soon appears that there are many more legends at play, as the various threads of the tale combine folklore from across the world into a Campbellian vortex. In the cantankerous voice of Valdimar Harladsson, Sjón has found the perfect counterbalance to Caenus’s Old Qfwfq-like narration, breathing new life into the strange myths.
Read more about Icelandic literature here.