So... is Manga Aesop Monogatari (TV) finished or not?
NO, it is not finished.
Why?
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Manga Aesop Monogatari follows the adventures of Aesop, a mischievous boy transported to a fantastical realm.
This new world is populated with mythical beings and talking animals, unlike anything he's ever seen.
Aesop's main goal is to discover a way back to his own, normal world.
His journey is filled with encounters with characters from famous fables and challenging situations.
Through these experiences, Aesop learns important life lessons along the way, developing as a person as he travels.