"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 around Akiha Shishidou, a high school girl living aboard the space station Midori no Hoshi. Akiha’s life takes a dramatic turn when she encounters Leopard, a sentient AI controlling a powerful mecha known as the Leopardon. Leopard, initially designed for combat, develops a unique personality and forms a bond with Akiha, who becomes its pilot.

The narrative unfolds as Akiha and Leopard navigate a series of conflicts involving various factions vying for control over advanced technology. Among these factions is the Galactic Alliance, a governing body seeking to maintain order, and the mysterious organization known as the Zodiac, which harbors its own agenda. Akiha’s journey is further complicated by her relationships with her classmates, including her childhood friend Itsuki Kannagi, who harbors feelings for her, and Honoka Kawai, a cheerful and supportive friend.

As the story progresses, Akiha discovers her own latent abilities tied to the mysterious "Space-Time Resonance" phenomenon, which grants her the power to manipulate space and time. This ability becomes crucial in her battles against enemies and in uncovering the truth behind the Leopardon’s origins. The series explores themes of identity, the ethical implications of AI, and the consequences of humanity’s reliance on technology.

The plot is driven by a mix of action, mystery, and interpersonal drama, with Akiha’s growth as a character serving as a focal point. Her interactions with Leopard and the people around her reveal her evolving understanding of responsibility, friendship, and the complexities of the world she inhabits. The series balances its futuristic setting with relatable human emotions, creating a narrative that is both engaging and thought-provoking.