Start with Under the Glacier. It runs under two hundred pages, it is very funny, and it is the cheapest possible way to find out whether Laxness suits you. A young emissary is sent by his bishop to a remote parish where the church has been boarded up, the pastor no longer performs services, and there is a persistent story about a body having been put into the glacier. He takes notes. Almost nobody answers a question directly. Susan Sontag admired the book enormously and wrote an introduction for it, which is how most English-language readers now arrive at it.
The obvious alternative is Independent people, and it is the wrong first move even though it is the better novel. It is the book behind the 1955 Nobel, and it is roughly five hundred pages of Icelandic sheep farming written to be relentless. Bjartur of Summerhouses will not be beholden to any man, and the novel spends its whole length showing what that stubbornness costs everyone who depends on him. Readers who begin there very often stop there. Learn the deadpan on a short book first and the long one becomes readable rather than punishing.
Start here
Under the Glacier was published in 1968, late in his career, and it is the most eccentric thing he wrote. The register is the point: a bureaucratic narrator recording absurdities without comment is exactly how Laxness handles tragedy too, only here nobody dies of it.
Follow it with The fish can sing (1957), about a boy raised by an elderly couple in a turf-roofed house on the edge of Reykjavik, with a famous singer circling the story from a distance. It is the warmest book he wrote and it has none of the cruelty of the major novels. Two short books in, the voice will be familiar.
The big one
Now Independent people, written across 1934 and 1935 and the reason he has a Nobel. It is a great novel about self-reliance as a moral catastrophe, and it is genuinely bleak — livestock die, children die, and the man at the centre keeps choosing his independence over the people in front of him. Nothing in the earlier two books prepares you for how hard it pushes. That is fine; by this point you will know the humour is still running underneath.
The historical novels
Iceland's Bell, written in three parts during the 1940s, is his most directly political book: seventeenth-century Iceland under Danish rule, a stolen bell, a man on trial, and a national question underneath all of it. Read it after Independent people rather than before, because the irony depends on knowing how he treats hardship when he is not being historical.
World Light, from the late 1930s, is the longest book on this path and the one his committed admirers name first. A pauper poet insists on beauty while everything around him is squalid. It is slower than the others and it rewards readers who have already decided they like him.
The satire
Finish with The Atom Station (1948), the short postwar novel about Reykjavik at the moment the Americans wanted an airbase. It is sharp, angry, and it made him enemies at home for years. Coming last, it reads as the political temperature underneath everything else on the list.
Should you just read him chronologically?
Chronological order would put World Light second and Under the Glacier last, and it is defensible if you are studying him rather than reading him — you would watch the socialist realism of the 1930s loosen into the strangeness of the 1960s. For a first pass it is the wrong shape, because it front-loads the two longest and hardest books. Read this order, then reread chronologically if he takes.
Where to stop
Three books is a complete experience: Under the Glacier, The fish can sing, Independent people. If the big novel defeats you, that is a common and reasonable outcome, and the two short ones stand entirely on their own. Much of the rest of his output — the Salka Valka novels, the late memoirs — is patchily available in English, so this path is close to what an English-language reader can actually get hold of.
More literary reading paths are on Discover.
Follow the full ordered path here: Halldor Laxness Reading Order: Where to Start with Iceland's Nobel Laureate.