So... is Azuki-chan finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: March 17, 1998
Manga finished: March 03, 1997
... But 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
Azuki-chan follows Azusa Noyama, a fifth-grader known by a nickname she isn't fond of.
Her life takes a turn when a new boy, Yuunosuke Ogasawara, arrives at her school and expresses his admiration for her nickname.
This simple interaction sparks a connection between them, leading to Azuki developing feelings for Yuunosuke.
The anime explores their budding relationship as they navigate the complexities of young love, sharing experiences and creating memories together.
At its heart, it's a charming story about first love and the everyday adventures of a young girl named Azuki.