So... is Babylon finished or not?
NO, it is not finished.
Why?
The anime finished after the manga:
Anime finished: January 28, 2020
Manga finished: October 07, 2019
... 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
Babylon follows Zen Seizaki, a prosecutor investigating a seemingly simple case of false advertising in the new Shiniki district of Tokyo.
His investigation quickly spirals into something much darker and more complex when he uncovers disturbing evidence linked to a mysterious anesthesiologist.
As Zen delves deeper, he uncovers a tangled web of corruption and deceit connected to the upcoming mayoral election and the very foundation of the Shiniki district itself.
Zen's pursuit of justice forces him to confront morally ambiguous situations and challenge his understanding of truth as he gets closer to a mysterious woman at the center of everything.
The series explores themes of morality, justice, and the blurred lines between right and wrong, as Zen navigates a dangerous landscape where the truth is constantly shifting.