The Girl Who Leapt Through Time chronicles the adventures of a high school aged girl, living in contemporary urban Japan, a safe enough environment, but not without dangers.
It's a coming of age story, of the kind my wife loved, on the surface a romance, but laced with metaphysics, a sense of wonder about time, the deep dimension, one might even say the only.
Makoto enjoys a rough and tumble lifestyle, to put it mildly, even without all that leaping. Girls have most of the freedoms of boys in this culture, relate as equals, although when it comes to after school drudgery, the guys tend to goof off (sound familiar?). She pushes her body to its physical limits, running, cycling... even studying.
Whereas a more somber soul might be plunged into an existential crisis by this new degree of freedom, Makoto takes it in stride, gradually building her power to solve triangles and otherwise "fix" things (shades of Groundhog Day), including for her own benefit.
She only gets really lonely when she finds someone to share it all with, but apparently misses the opportunity. Anyway, she still has her wise auntie to console her. I won't give away the (happy enough) ending.