So... is Kyou, Koi wo Hajimemasu finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: October 23, 2010
Manga finished: February 03, 2012
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
Kyou, Koi wo Hajimemasu centers on Hibino Tsubaki, a studious and traditional girl who finds her life disrupted when she encounters Kyouta Tsubaki, a rebellious and popular classmate.
Despite being top students, they are polar opposites. Kyouta's teasing and provocative behavior clashes with Hibino's reserved nature.
The story explores the unexpected connection that forms between them, hinting at a potential romance that blossoms despite their initial animosity and contrasting personalities.
The anime focuses on their journey as they navigate the complexities of high school life and the budding feelings that challenge their preconceived notions about each other.