More commonly known for his short story "The Cold Equations", which has been infuriating people who think life is fair and kind for 65 years, he wrote a number of other novels and short stories. I've read this probably 20-30 years ago, but not as a single piece since then.
Spoilers ahead, go read the book, it's VERY short, a novella by modern standards.
Earth is being blockaded by an alien empire called the Gern, a colony ship of 8000 is sent to a newly-discovered planet Athena with rich resources which can be used to make weapons protecting Earth. They're defeated and half the population are set down on an inhospitable high-gravity planet Ragnarok, the other half taken as slaves to Athena to work for the Gern.
The Gern (derived from Hugo Gernsback?) caricature is, uh, problematic:
"The were big, dark men, with powerful, bulging muscles. They surveyed her and the room with a quick sweep of eyes that were like glittering obsidian, their mouths thin, cruel slashes in the flat, brutal planes of their faces."
… (much later) …
"Narth, like all the Gerns, was different from what they had expected. It was true the Gerns had strode into their town with an attempt at arrogance but they were harmless in appearance, soft of face and belly, and the snarling of the red-faced Narth was like the bluster of a cornered scavenger-rodent."
Well. And none of the Earth people are described in any racial way, except one Germanic psychopath.
As for the Humans, most of the "rejects" left on Ragnarok die in the first few days and are whittled down over years to 49, before the new generations acclimated to the gravity and atmosphere, harsh conditions, and carnivorous diet increase back up to 6000+ over another 200 years, which requires a rather high birth rate and low death rate; I don't think it's quite plausible.
It's notable that the first viewpoint character is a woman. She doesn't last long, and after that few women even get to speak, only one about anything except babies, and most of them die young. The final state of the Ragnarok barbarians is a totalitarian tribal society where women and children hide in caves, men go fight; the women are physically and mentally competent, as shown in one animal fight scene late in the book, but not consulted in war.
The transmission of knowledge, in a handful of books somehow written and preserved by these not-quite-paleolithic barbarians, is exceedingly implausible. They make technical and scientific leaps which would be extraordinary in societies of billions, let alone a few thousand. Meanwhile neither Earth nor the Gern make any technical progress in the 200 year course of the book, allowing ancient written knowledge of their blasters and ship systems to help 10th generation barbarians.
I'm not going to criticize a book from the '50s for having FTL drives and communications, but I roll my eyes at it anyway, especially when they propose building spaceships and FTL communicators with stone knives & prowler-skins, as it were.
Native life of Ragnarok consists of: Prowlers (wolf/big cat type hunters), Unicorns (psychotic bison with one horn), Wood Goats, a few species of small and large scavengers, and Mockers (telepathic squirrels), and plants not dissimilar to Earth. It's not much of an ecosystem, and is never explained sufficiently. To some extent, Godwin didn't understand the ecological energy pyramid. I have an untested, almost unsupported hypothesis that the erratic orbits of Ragnarok and its suns may be a post-apocalyptic situation, where these are the few survivors of a more complex ecosystem; that would help explain the intelligence of the few survivors.
They have a series of strong male leaders, willing and able to execute anyone who doesn't share everything with the group, are incorruptible, and single-minded on survival and the long-term ideal of defeating the Gerns. This is, to be blunt, maybe the least plausible thing. I can buy one or two such leaders, but getting a third is beyond impossible. Humans fuck everything up with politics and religion, there's no way they wouldn't.
The barbarians do make good use of all their resources, despite an almost total lack of metals on the planet. And yet at no point are cannibalism or hierarchical resource distribution discussed, which are the usual Human solutions to extremely tight resources. The Aztecs would be very disappointed in Ragnarok.
The rapidity of them adapting to spaceship technology and developing a new tactic against an ancient spacefaring empire is very unlikely; ridiculous, even.
And here's the thing, most of this I can criticize as unrealistic. But the idea of a Hell world breeding up super-soldiers who then seize power from the civilized and establishing their own Empire, that's an idea that appears in many other places.
Historically, the Spartans tried to make this work, despite being in one of the most fertile and pleasant places on Earth, and did make superior warriors… at a cost of crippling their economy and culture, and eventually twice being defeated by coalitions of everyone else in the region who hated them for it.
Germanic barbarians lived in much more difficult environments and had more meat-heavy diets than the Romans, and were physically more powerful; but that generally didn't help them win wars against civilized people until Rome started collapsing for internal reasons (maybe lead pipes, but just as much the abandonment of military traditions by filthy ignorant Christians).
The Zulu Empire rose with Shaka Zulu and his Spartan-like ideals, and almost immediate collapse after his murder by his idiot brother. South Africa ranges from Hell world to some of the most fertile places on Earth, so there wasn't an environmental pressure, only one strong leader.
So the reality of this idea does not work.
In Dune, obviously, with both the Fremen and Sardaukar. The Fremen women, unlike the Ragnarok barbarians, fight like the men do, and Leto II's Fish Speakers, descended from both Fremen and Sardaukar, are all women. Herbert revisits this in The Dosadi Experiment, though the Dosadi survivors are more politically treacherous than superhumanly dangerous.
Harry Harrison's Deathworld series has easily the most dangerous planet, vaguely habitable but every form of life trying to kill invaders, but the successful colonists adapt to the environment, rather than trying to fight and control it.
I honestly don't know how to rate this. It's a very enjoyable read, but there are so many cultural, literary, political, ecological, and technical things I object to that it shouldn't pass.
★★☆☆☆ / ★★★★☆ depending on how I think about it.
There's a sequel, The Barbarians, which I'll likely read soon, and see if that addresses anything or makes it worse.