So... is Kotoura-san finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: March 29, 2013
Manga finished: March 26, 2015
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Kotoura-san tells the story of Haruka Kotoura, a young girl burdened with the ability to read minds.
This power isolates her from others, leading to a lonely and withdrawn existence.
However, when Haruka transfers to a new school, she encounters Yoshihisa Manabe, who accepts her ability rather than shunning her.
Yoshihisa's friendship sparks a turning point in Haruka's life.
The anime follows Haruka as she learns to navigate social interactions, builds friendships, and confronts the challenges of her unique ability while opening her heart to those around her.