So... is Tokyo Daigaku Monogatari finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: March 24, 2004
Manga finished: January 01, 2001
... But MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Tokyo Daigaku Monogatari centers around Murakami Naoki, a brilliant high school student who finds himself deeply infatuated with Mizuno Haruka.
He unexpectedly begins a relationship with her, and they enjoy a romance that seems destined to face challenges.
The core of the story revolves around their shared goal: gaining acceptance into Tokyo University.
The narrative explores the potential impact of their individual exam results on their relationship, specifically posing the question of what might happen if only one of them succeeds in entering the prestigious university.