"Extra Olympia Kyklos" is a science fiction anime series set in a distant future where humanity has colonized multiple star systems. The narrative centers on the Olympia System, a cluster of planets governed by a powerful federation known as the Kyklos Alliance. The Alliance maintains control through advanced technology and a rigid hierarchical structure, but dissent brews among the outer colonies, which suffer from resource exploitation and political neglect.

The protagonist, Aria Valen, is a skilled pilot and former Alliance officer who becomes disillusioned with the Kyklos regime after witnessing the suffering of the outer colonies. Aria joins a rebel faction called the Ecliptics, a group of freedom fighters determined to dismantle the Alliance's oppressive rule. Alongside Aria are key allies: Kael Orion, a brilliant but reclusive engineer who designs cutting-edge technology for the rebels; Lyra Solis, a former diplomat with deep knowledge of the Alliance's inner workings; and Zane Vortex, a charismatic but unpredictable mercenary with a personal vendetta against the Kyklos leadership.

The plot unfolds as the Ecliptics launch a series of covert operations to disrupt the Alliance's supply lines and expose its corruption. Their efforts escalate into a full-scale rebellion when they discover a secret project called Olympia Nova, a superweapon capable of annihilating entire planets. The Alliance intends to use Olympia Nova to crush dissent and solidify its dominance, forcing the Ecliptics to race against time to sabotage the weapon and rally the colonies to their cause.

As the conflict intensifies, the series explores themes of loyalty, sacrifice, and the moral complexities of revolution. Aria and her comrades face difficult choices, balancing their ideals with the harsh realities of war. The narrative also delves into the personal histories of the main characters, revealing how their pasts shape their motivations and relationships. The climax of the series involves a decisive battle for control of Olympia Nova, with the fate of the Olympia System hanging in the balance. The story concludes with an open-ended resolution, leaving room for potential future developments while providing a satisfying conclusion to the central conflict.