The gigantic, cylindrical generation ship Vanguard, originally destined for Proxima Centauri, is cruising pilotless through the interstellar medium as a result of a failed mutiny that killed all of the piloting officers. The descendants of the surviving crew have forgotten the purpose and nature of their ship over time and lapsed into a pre-technological culture infested with superstition. Most crew members lead a simple illiterate life of farming, never venturing to the "upper decks" where the "muties" (mutants or mutineers) dwell. These descendants of the loyalists — who live in the lower, outer levels of the cylinder — believe their world is the entire Universe, not realizing they live inside a spaceship. They are ruled by an oligarchy of "Officers" and "Scientists", whose head is the putative heir or successor of the original Captain.

They still use the term "The Ship" for where they live, but it has come to mean "The World" or in fact "The Universe" so that "To move the ship" is considered an oxymoron. Old texts talking of "The Voyage" are interpreted as a metaphor for the voyage from birth to death.
The 1951 Dell printing of "Universe"

The story is told from the perspective of an unusually intelligent and curious young man, Hugh Hoyland. Hugh has been selected to apprentice to the ranks of the Scientists, who ritualistically perform the technical tasks needed to keep the ship running (such as "feeding" trash into the power converter for lighting and environmental control). While on a mission to hunt down muties, Hugh is captured and taken to the inner, low-weight, mutie-controlled levels. He becomes the slave of Joe-Jim, the two-headed leader of a powerful gang of muties. Joe and Jim are very intelligent and, having read a vast amount of books, have some concept of the true nature of the universe. They share this with Hugh by taking him forward to the bridge and letting him look outside the ship through the windows in the "Captain's Veranda."

This revelation is an epiphany for Hugh. He convinces Joe-Jim they should complete the Vanguard's mission and navigate the Ship to its intended destination (preserved in fable as "Far Centauri"). Hugh then returns to the human-inhabited levels to convince others to help him. He starts with his former boss, Bill Ertz. Bill has him arrested for blasphemy. He is put on trial and is sentenced to death. While in his cell, he is allowed to see his old friend, Alan Mahoney. Alan is willing to help. Hugh has him go to the upper levels, where he convinces Joe-Jim to mount a prison break. The gang captures Bill on their way back to mutie territory. Later, Hugh takes Bill and Alan to see the universe from the Captain's Veranda. Bill realizes that he was wrong and agrees to help Hugh. With Bill's help, the group is able to convince the captain's aide, Phineas Narby, to join the effort.

Inspired by one of Joe-Jim's books, The Three Musketeers, the group create swords and armor which are superior to anything the normal humans have. They incite a rebellion among the younger Scientists and overthrow the old Captain. Phineas becomes the Captain, Joe-Jim the Vice-Captain, Bill the Chief Engineer, and Hugh the navigator, or astrogator, of the Vanguard. However, Phineas never believed Hugh's story and only used the others to grab power. No longer needing them, he incites an attack to rid the Ship of all muties. In the fighting, Joe is killed by a throwing knife. Upon realizing this, Jim sacrifices himself to hold off their pursuers long enough for Hugh and his followers to retreat to a lifeboat (whose builders had taken into account that later generations might have little training). They manage to leave the Ship and land on a moon of a gas giant planet. By sheer luck, the moon turns out to be habitable.