The first two months went by pretty quickly. Hermione was learning a lot. She has proven herself to be the brightest and smartest amongst her class, which did not bode well for her friendships in Ravenclaw. You'd think that a house which values wisdom and intelligence would value a student like Hermione, but her fellow Ravenclaws, who all wanted to be the smartest and brightest, only perceived her academic excellence as a threat. If she was to be honest, it did bother her a little. She was hoping Hogwarts would be different from her old school in that regard, but it wasn't.
That's okay though, she still had friends outside of Ravenclaw. She was friends with Neville, the boy who lost his toad on the train. She would hang out with him and, occasionally, Ron Weasley. Ron mostly hung out with the two other Gryffindor first-year boys, Seamus Finnigan and Dean Thomas, but he would also hang out with Neville and Hermione whenever the other two weren't around. Hermione and Ron did not get along very well.
She also befriended Harry Potter from Slytherin. They sometimes end up on the same table in Herbology, but they don't hang out much outside of classes. He spends most of his time with Draco Malfoy, with whom Hermione had limited, but mostly unpleasant, interactions.
But still, she would sit alone for breakfast, lunch, and dinner. She would still sit on her own in most classes. She would spend most of her free time alone, studying, in the library. She avoids the Ravenclaw common room altogether these days.
It was around midnight that night, the night before Halloween, that she noticed the time. "Shit!" She's out after curfew. She closes her books, and just sweeps everything off the table into her bag. She grabs it, and runs out of the library and towards the Ravenclaw tower. As she's going up the stairs in the darkness, very quietly so as to not get caught, she accidentally takes one of the moving stairs, and it starts moving. "Oh no! Oh no! Oh no!" She whispers to herself, but still loud enough for somebody to hear.
"Did you hear this Mrs. Norris?" Hermione heard a voice from afar. Shit! That's Filch. She cannot get caught. She runs up the stairs, and into the nearest corridor. After running for a little while, she decided to go hide inside one of the classrooms. She takes a right, and tries to open the first door, but it's locked. "Are we about to catch a student out of bed, Mrs. Norris?" She hears steps coming towards her. She takes out her wand, points it at the door lock, and whispers "Alohomora!" The door is wide open now. She enters the room, and closes the door behind her, quietly enough not to bring attention to her hiding spot. Then she listens through the door as the steps get closer, and then farther. What a relief!
She takes a few seconds to recover from the experience. She almost got caught! And God knows what the consequences would've been… She could've been expelled! She hears something breathing behind her. Could that be Filch?!
She turns around slowly, and finds herself face to face with a three headed dog. Straight out of Greek mythology. Had the dog not been intimidating, it would've been fascinating! Does the existence of a cerberus confirm Greek mythology and imply the existence of Greek gods such as Hades, or even the Underworld?!
But that was not the time for Hermione to geek over this majestic beast, because in no time it would decide to make dinner out of Hermione. She's too stunned to scream her lungs out, but she gathers all the courage found inside her to slowly, so as to not spook the cerberus, open the door and get out of there.
That was spooky. She realized that was the third-floor corridor. The corridor which students should avoid unless they "wish to die a very painful death." What the…
Hermione makes her way back to the Ravenclaw tower mostly uneventfully, except for having to hide behind a statue to avoid Snape and Quirrell. When she got to the dorms, all the Ravenclaw first-year girls were chattering and giggling about something. She tries to join, but she only gets some weird looks from her dorm-mates. So she heads to bed.
She couldn't fall asleep that night. She was thinking of the cerberus. He was standing on a door. Whatever's under that door, the cerberus is guarding it. Which is only fitting, given cerberus guards the Underworld in Greek mythology. Dumbledore really wants to keep students away from whatever's under that door. But, what is it?