"Square of the Moon" is a supernatural mystery anime that centers around a young protagonist, Haruto Aizawa, who discovers an ancient artifact tied to a forgotten lunar ritual. The story begins when Haruto, a high school student with an interest in astronomy, stumbles upon a peculiar stone tablet in his family’s attic. The tablet bears cryptic symbols and a depiction of a square overlapping a crescent moon. After deciphering part of the inscription, Haruto inadvertently activates a dormant power, drawing the attention of a secretive organization known as the Lunar Order. This group has been searching for the tablet for centuries, believing it holds the key to unlocking a celestial event that could alter the balance between the human world and the spirit realm.

As Haruto delves deeper into the mystery, he encounters a diverse group of allies, including Rina Takahashi, a classmate with a hidden connection to the Lunar Order, and Kaito Morimoto, a rogue spirit hunter who initially opposes Haruto but later becomes a reluctant ally. Together, they uncover the tablet’s purpose: it is one of four relics needed to perform the "Square of the Moon" ritual, a ceremony said to grant immense power but at a great cost. The ritual requires the alignment of the four relics during a rare lunar eclipse, and failure to complete it correctly could unleash catastrophic consequences.

The narrative unfolds through a series of episodic adventures as Haruto and his companions travel to various locations to retrieve the remaining relics. Each relic is guarded by powerful spirits or traps, and their acquisition often involves solving intricate puzzles or confronting personal challenges. Along the way, the group learns about the history of the Lunar Order, which was founded by a group of ancient astronomers who sought to harness the moon’s energy but were ultimately betrayed by one of their own, leading to the ritual’s abandonment.

As the lunar eclipse approaches, tensions rise within the group. Rina’s loyalty is tested when she discovers her family’s dark ties to the Lunar Order, while Kaito struggles with his own motivations for aiding Haruto. The final arc of the series culminates in a dramatic confrontation at the ritual site, where Haruto must decide whether to complete the ritual or destroy the relics to prevent the potential destruction of both worlds. The story concludes with a bittersweet resolution, leaving some questions unanswered while providing a satisfying conclusion to Haruto’s journey of self-discovery and growth.