Where does Hermione start?

Book 1: Hermione is insufferable in the best way. She memorized the curriculum before arriving. She corrects professors. She informs Harry and Ron of rules they're breaking while helping them break the rules. She has no friends because her competence makes people feel inadequate rather than elevated. She is, in her own way, lonely.

What changes her?

Being accepted for who she is. When Harry and Ron save her from the troll and she lies to protect them, the friendship becomes real. After that, her social world expands — not by becoming less herself but by being herself with people who appreciate it rather than resent it.

What is her arc in the middle books?

She broadens from excellent student to excellent person. She advocates for house-elf rights when everyone else ignores or mocks it. She manages the DA's organizational logistics. She perceives Umbridge accurately when others doubt themselves. She also makes mistakes — her campaign for house-elf rights is condescending in ways Dobby himself points out. Growth includes acknowledging those failures.

What is her arc in the final books?

Taking initiative in ways that require trusting herself. She modifies her parents' memories and sends them to Australia — one of the most quietly devastating choices in the series. She plans for the Horcrux hunt methodically while Harry and Ron spiral. She's the logistical spine of the final quest, not because she's bossy (the old critique) but because someone has to be.

How does she grow as a person, not just a student?

She learns that being right isn't enough. Right + connected + flexible is what the situation requires. By Deathly Hallows she's capable of emotional nuance she couldn't access in Philosopher's Stone. The knowledge hasn't changed; her relationship to people has.