"The Panchatantra is a collection of children's stories, like Aesop's fables."
This statement is false.
Neither in its original design and intent, nor in its structure, is Panchatantra a set of children's stories.
Panchatantra is a treatise on statecraft that uses animal stories as pedagogy.
The animals are used as metaphors of human characteristics.
The stories are neither childlike nor non violent. They encompass every element of human emotions and interactions. There is deceit, violence, death, flattery, coercion, persuasion, betrayal, et al.
The Panchatantra should be read to understand statecraft.
If that holistic view is of any use to you, the National Book Trust has a book that has all the stories of Panchatantra, in order, with the lesson attached to each.
There is also another book that just lists the suktis or sutras in order. You can also refer that one. (Different publisher).
None of the sutras is useful by itself. It has to be viewed in context. Which is why, when I tried to read only the sutras book, it was not as useful. But read with the context of the stories, they made a lot of sense.