Iceland publishes more books per head than almost any other country, and the national appetite for reading goes deep. A few that help you see Reykjavik from the inside:
Halldór Laxness — The Atom Station. Laxness won the Nobel in 1955 and most of his novels are set in Iceland; The Atom Station (1948), about a country girl who comes to work as a maid in a Reykjavik MP's house in the 1940s, is the funniest and most political. The version of Reykjavik in it — a small capital coming to terms with American military bases and modern money — is half-recognisable in the current city.
Halldór Laxness — Independent People. The country novel rather than the city one, but the book everyone reads first to understand Iceland. Bjartur of Summerhouses' lifelong stubborn struggle to be free of debt is the founding myth of the modern Icelandic personality.
Arnaldur Indriðason — Jar City (and the rest of the Erlendur series). The Icelandic detective novel that put Reykjavik crime fiction on the map. The detective Erlendur works through a series of cases in a city where everyone is two phone calls from everyone else and the past keeps surfacing into the present.
Sjón — The Blue Fox. A short, strange, lyrical novella by the Icelandic poet who has also written most of Björk's lyrics. Reads almost like a folk tale; tells you something about the Icelandic way with language and landscape.
Andri Snær Magnason — On Time and Water. Part memoir, part climate writing, part family history. Magnason is one of contemporary Iceland's clearest writers on the country's relationship with its glaciers, its hydropower and its future.