Our Hats is a kind of fantasy, with a modern, urban setting. Saki and her mother move into an old apartment building while their home is being renovated. At first, Saki feels downcast at living in the old building; but soon she comes to feel an interest in it. In a cupboard in the apartment she finds a patchwork hat, made of bits of cloth with flower and leaf patterns. She tries the hat on and is still wearing it when her pet bird, Chiruru, gets out of its cage and flies out of the open door of the apartment. Chasing the bird, she climbs the stairs to the fifth floor, where she finds the door of another apartment open and hears a voice quietly singing inside.
In the middle of the all white, empty, bright room a girl was standing, facing to one side. She was wearing a white blouse and a fluffy round green skirt. Not just that, on top of her shoulder length curly hair, wasn't that the same hat as Saki was wearing? And then, sitting on her fingertip, there was Chiruru. He had his head on one side, just as if he was listening to the girl's song.
Saki becomes friends with the mysterious girl, Iku. Wearing their nearly identical hats, the two explore the building, with its strange corridors and stairs, and observe the even stranger residents. Saki keeps her friendship a secret from her mother, as she suspects that there is something strange about Iku.
The book keeps a balance between reality and fantasy, using the mysterious feeling that a strange older building has for young children. Saki's interpretation of the building and the people in it is informed by the expectations of a child who has read fantasy stories; but most of what she witnesses could be interpreted as part of the (not very) normal world. She has competing desires, for a normal friendship with a real girl her age, and for mysterious and magical events. The resolution of the various puzzles satisfies both her wishes in an unexpected way and links the friendship across the building's history.
[I borrowed the illustration from the JBBY web site that I link to. Mostly I put up a scan of the cover of the books I discuss. But since in either case the copyright belongs to someone else, I hope that if anyone has a problem, they'll let me know, so that I can remove it.]