Anathem is set on and around the planet Arbre. Thousands of years prior to the events in the novel, society was on the verge of collapse. Intellectuals entered concents, much like monastic communities but focused on intellectual endeavors rather than religious practice. Here, the avout— intellectuals living under vows and separated from Sæcular society, fraa (derived from Latin frater) for male avout and suur (derived from Latin soror) for female avout — retain extremely limited access to tools and are banned from possessing or operating most advanced technology (at a level beyond paper and pen) and are watched over by the Inquisition, which answers to the outside world (known as the Sæcular Power). The avout are forbidden to communicate with people outside the walls of the concent except during Apert, a 10-day observance held only once every year, decade, century, or millennium, depending on the frequency with which a given group of avout is allowed to interact with the Sæcular world. Concents are therefore slow to change - unlike the rest of Arbre, which goes through many cycles of booms and busts.
Interaction between the avout and the Sæcular world is not, however, limited to Apert. The secular power may "Evoke", or remove from the concent, members of the avout, when needed to address pressing scientific ("theorical") issues facing Sæculars. Such removal is one of many "Auts" (ritual acts) performed on certain occasions – much like rituals or sacraments of the Roman Catholic Church. The act of removing an avout from a concent at the request of the Sæcular Power is called "Voco" (a Latin word meaning "I call": most of the technical words used in Anathem are derivations or puns on Latin words, cf. Lucub – a late-night study session – from the Latin lucubratio), or "evocation", the avout called being "evoked".
The narrator and protagonist, Erasmas, is a fraa at the Concent of Saunt Edhar (Saunt, abbreviated St., is a corruption of the ancient word savant and is a title bestowed on influential intellectuals of the past). His primary teacher, Orolo, discovers that an alien spacecraft is orbiting Arbre — a fact that the Sæcular Power attempts to cover up. Orolo secretly observes the alien ship with a video camera which is prohibited by Cartasian Discipline. Erasmas is unaware of the content of Orolo's research until he deciphers it after Orolo is banished in a rite called Anathem (cf. the Christian rite of bell, book, and candle anathematization) as the result of his possession and use of proscribed technology within the concent.
The law of the Second New Revised Book of Discipline that governs the lives of the avout at the time of the narration – which bans the avout from owning anything but two pieces of clothing and a sphere with multiple uses, and bans them from using or even knowing how to use any technology but paper and pen – was developed in response to the third large-scale plundering of concents by the Sæcular world, which itself was initiated due to the Sæcular belief that certain avout, especially of the Millenarian Maths, had developed a praxis (technology) that required nothing more than the mind, and was (depending on a specific avout's inclination or area of study) able to effectively change the past ("the Rhetors") or the future ("the Incantors") through an unknown method, making it much more powerful and dangerous than any "real" technology. It was later recognized as some sort of many-worlds interpretation "narrative shifting", in being able to shift consciousness – which is hypothesized as the driving force behind reality, as something is not measurable until it is observed in quantum theory, thus a phenomenon called wave function collapse occurs from many cosmos very similar to the "real" one. This is made possible because the mind is found to inhabit many slightly different cosmos, and moments of thought where everything "falls into place" are recognized as the mind's reaction to waveform collapse.
There is much discussion of a methodology by which narrative shifting occurs. In general it is centered on the idea that information may flow between different worldtracks (known in the books as "Narratives") via a method modeled using directed acyclic graphs, in which information may only flow in one direction. This premise, which is discussed in an appendix (a "Calca"), is key to understanding later events in the book.
Several months pass, and Erasmas falls in love with Suur Ala, another avout at Saunt Edhar. Immediately after this, the Sæcular Power removes (Evokes) her along with several other avout, and Erasmas expects never to see her again. Erasmas, still upset about Orolo's banishment, throws himself into his work. The presence of the alien ship soon becomes an open secret among many of the avout at St. Edhar. Several weeks later, a laser shines down from the ship and illuminates the Millenarian Math of Saunt Edhar. Now that the aliens have shown themselves openly, the Sæcular Power evokes many avout from Saunt Edhar, this time including Erasmas himself, along with one Millenarian - Fraa Jad.
Erasmas and the rest of the avout are told to travel to the concent of Saunt Tredegarh, two thousand miles away. But Erasmas and some like-minded avout also desire to find Orolo first, and subsequently enlist a few extramuros (non-avout) volunteers (including Erasmas' sister Cord) on an unauthorized journey to Bly's Butte, where they think Orolo has traveled to continue his astronomical observations. Upon arriving there they discover that Orolo had already left for a destination unknown. Fraa Jad urges Erasmas to continue his search for Orolo towards the North (over the frozen pole of Arbre), suggesting that Orolo has valuable information about the aliens. Erasmas agrees and sets off with just three companions to pursue Orolo, while the others turn back and head to Tredegarh. Along the way, they determine that Orolo's destination is likely to be the isolated former concent of Orithena, far in the opposite hemisphere of Arbre. They also acquire another companion named Yulassetar Crade, a tough wilderness guide with skills important for their trek. By this time, the aliens have come to be known as the Geometers because of a graphical proof of Pythagoras' Theorem (which in the world of the book is referred to as Adrakhones' Theorem) seen inscribed on the hull of their ship.
After a dangerous journey over the planet's frozen pole, Erasmas and his comrades eventually arrive at a concent-like establishment called Orithena, and reunite with Fraa Orolo. Orolo holds discussions with Erasmas about the nature of the cosmos and consciousness, and how he believes that the Geometers are not simply from another planet, but from another cosmos which is influenced by Arbre. During the discussions between Orolo and Erasmas, a small spacecraft lands on Orithena. A female Geometer is on board, but dead of a recent gunshot wound. She brings with her four vials of blood — presumably that of the Geometers — and much evidence about their technology. Shortly thereafter, the Geometers propel a massive metal rod at a nearby volcano, triggering an eruption which destroys Orithena. Orolo sacrifices his life to ensure the safety of the dead Geometer's remains, an event that leads to his canonization as Saunt (Savant) Orolo.
Erasmas soon arrives at Saunt Tredegarh, which is home to a joint conference (convox; from "convocation", meaning "speaking together") of the avout and the Sæcular Power dedicated to dealing with the military, political, and technical issues raised by the existence of the alien ship in Arbre's orbit. Tredegarh is where the Sæcular Power had brought many of the evoked avout of Saunt Edhar (including suur Ala) to work on methods of collecting and interpreting the limited information regarding the alien spacecraft, as well as researching possible military options. Much research is done on the Geometers, who are found to come from four planets in four distinct parallel worlds (cf. Many-worlds interpretation): Urnud, Tro, Fthos and Laterre ("The Earth" in French: "La Terre"). Through observation and experiment, Erasmas and his companions determine that the conference is infiltrated by the aliens, and unmask a Laterran linguist - Jules Verne Durand, known to them as Zh'vaern. He explains that the Geometers are experiencing internal conflict between two factions. The currently ruling faction intends to attack and raid Arbre for its resources in order to repair their spaceship, while the opposing faction favors open negotiation. Jules Durand offers to assist the avout of Arbre in resisting the ruling faction of the Geometers, believing that they can bring the situation to a peaceful conclusion.
Under fear of a Geometer attack due to the uncovering of the infiltration, the avout flee Saunt Tredegarh and the other concents on Arbre, dispersing into the Anti-Swarm (an organized dispersal of the avout throughout the planet, amongst regular society). Erasmas and several of his old and new avout friends are taken to a distant sanctuary, where they receive training for a mission to board the Geometers' ship — the Daban Urnud — and disable its weaponry. They are launched into space, unknowingly bringing with them "Everything Killers" (Neutron Bombs), which the Sæcular Power intends to use as a last resort should the explicit goal of the avouts' mission fail. Three people — including Fraa Jad — are issued detonators.
The avout team boards the ship and the narrative of the novel splits several ways, in keeping with the book's theory of multiple parallel universes. Several avout trained in martial arts destroy the ship's main weapon, perishing in the attack. In one Narrative, Fraa Jad leads Erasmas into the command center of the "Daban Urnud", where it emerges that the Millenarian avout of one thousand years in the past may have used their "incanting" powers to summon the ship to their cosmos from another parallel (or higher?) one. In yet another Narrative, Jad opens a door into a protected area and, upon being attacked, triggers the Everything Killers; Erasmas dies and the population of a section of the Daban Urnud starship are killed.
In the final Narrative (the one that continues ahead) Erasmas awakens in a hospital on the starship to the perplexing news that Fraa Jad had died soon after their launch, contradicting his obvious presence and memories up to that point. It remains unclear which (or how many) of these contradictory narratives is real, and what may have happened in different worldtracks that have crossed and overlapped. However, Fraa Jad had hinted that the Incanters (and possibly Rhetors) were capable of operating simultaneously in parallel universes, so Jad is likely to have survived in other world lines.
Erasmas discovers that the Geometers have brought up a high-powered delegation from Arbre, including Ala and his sister Cord. A funeral ceremony for those lost on both sides of the attack forms part of the signing of a peace treaty between the "aliens" and the Arbrans. On Arbre itself, the Sæcular Powers and the avout have agreed to cooperate as equal powers. The people of Arbre inaugurate a second historical "Reconstitution", revising many of the rules that had restricted the work and lifestyle of the avout (which included drug-induced sterility). Erasmas and friends set about the task of building a new concent, though they do not call it such, as a temple dedicated to Saunt Orolo. The closing scene is a rousing double wedding, with Erasmas marrying Ala, and his sister Cord marrying Yulassetar Crade.