Ryland Grace wakes from a coma aboard a spaceship with no memory. He discovers his dead crewmates and begins to piece together where he is. Interspersed flashbacks reveal the discovery of Astrophage — an alien organism consuming the Sun's energy — and Grace's recruitment by Eva Stratt.

Grace explores the ship, catalogs his resources, and begins the scientific work of studying the Tau Ceti system. Flashbacks reveal the development of the Hail Mary project and the selection of the crew.

Grace detects an alien ship in the Tau Ceti system. He makes contact with Rocky, an Eridian engineer whose star faces the same crisis. They begin the painstaking process of building a shared language from mathematics.

Grace and Rocky combine their knowledge to investigate why Tau Ceti is unaffected by Astrophage. They discover the planet Adrian and the predator organism — Taumoeba — that keeps Astrophage in check. Scientific and engineering challenges multiply.

Taumoeba must be tested to confirm it can survive in the environments of both Earth's and Erid's star systems. Experiments fail. Cultural and biological differences create unexpected complications. Grace confronts his own cowardice in flashback.

After numerous failures, Grace and Rocky engineer a Taumoeba strain that can survive in both stellar environments. They successfully culture enough to seed both star systems. But a new crisis emerges: Rocky's ship is damaged.

Grace chooses to repair Rocky's ship, knowing it means he cannot return to Earth. He sends Rocky home with Taumoeba samples for both Erid and Earth. Grace remains in the Tau Ceti system, alone, expecting to die.

Grace does not die. The Eridians, following Rocky's return, send a rescue ship. Grace is recovered and brought to Erid. He becomes a teacher again — this time teaching Eridian children about Earth science. The novel ends in a classroom.