"The Girl Who Leapt Through Space" is a science fiction anime series set in a futuristic universe where humanity has expanded into space. The story centers on Akiha Shishidou, a high school girl living aboard the space station Midori no Hoshi. Akiha possesses a unique ability to communicate with the station's AI, Leopard, which governs the station's operations. This connection becomes pivotal as the narrative unfolds.

The plot begins with Akiha's ordinary life being disrupted when a mysterious object, later revealed to be a sentient AI named Imo-chan, crashes into the station. Imo-chan bonds with Akiha, granting her the ability to "leap" through space, effectively teleporting across vast distances. This ability draws the attention of various factions, including the military organization A-TEC, led by Akiha's older brother, Itsuki, and the enigmatic group known as the Serpent Masters, who seek to exploit Imo-chan's power for their own purposes.

As the story progresses, Akiha becomes entangled in a conflict involving the Serpent Masters, who aim to destabilize the balance of power in space. The narrative explores themes of coexistence between humans and AI, the ethical implications of advanced technology, and the responsibilities that come with power. Akiha's journey is marked by her growing understanding of Imo-chan's origins and the broader implications of their bond.

Key characters include Akiha's classmates, such as the cheerful and resourceful Honoka Kawai and the reserved but loyal Kazane Hishikawa, who provide both emotional support and practical assistance. Itsuki Shishidou serves as a protective figure and a bridge between Akiha and the larger political forces at play. The Serpent Masters, led by the cunning and manipulative Leon, act as the primary antagonists, driving much of the conflict.

The series balances action, drama, and moments of lightheartedness, with Akiha's personal growth and relationships forming the emotional core. The narrative builds toward a climactic confrontation that tests Akiha's resolve and her ability to wield her newfound powers responsibly. Through its exploration of futuristic technology and human connections, "The Girl Who Leapt Through Space" presents a compelling story set against the vast backdrop of space.