Nearly half of this little book is a literary and historical analysis, though if you've read at least a few of the MLA Texts and Translations books, it won't come as much of a surprise. As other reviewers have said, the author of this book was the first woman in Russia - and all of Europe - to earn a doctoral degree in mathematics (though she did not earn the degree itself in Russia - higher education was essentially unobtainable for women at the time). Because Kovalevskaya turned to literary pursuits mostly as she became older, she left mostly scraps and short literary works behind when she died an untimely death at 41 from "complications of a bronchial infection" (pg xvi).
At most, this was a quick read about the author-narrator's relatively short (yet sometimes intimate) friendship with a girl name Vera Barantsova, the daughter of a count, who, by the tales we hear of her upbringing, becomes a "nihilist girl." (Apparently, the term "nihilist" carried a different meaning in the mid 1800s in Russia: it had come to signify a movement of social change where the goal was to radically change the "backward" customs and policies of tsarist Russia.)
Though Vera searches in vain for a way to contribute "to the cause," imagining potential allies everywhere, she eventually finds her "mission" is to try and save many through her devotion to one, a Jewish medical student who is to be thrown in an awful prison in St. Petersburg where no mercy will await him. By her rash actions and some string pulling/favor calling among her high-up family ties, Vera gives up the promise of her own life through tethering herself to a political prisoner in far-away Siberia.
The narrator, who is described in the earlier literary analysis as belonging to an earlier generation of upper-class, educated nihilists, does not understand why Vera has gone through such pains to soften the sentence of a man she barely knows and does not love: the narrator's cohort of idealists believe true social progress comes from individual enlightenment through education. Even as the narrator tries earlier on in the book to entice Vera with the promise of education (for Vera is, through the fault of her parents and the aftermath of the freeing of the serfs, very poorly educated indeed), the latter sees no point in studying a fly's eye when she knows the common man is out there somewhere, suffering. That point was poignant for me, because even as the narrator pities Vera's underdeveloped faculties that led to this chain of thought, there is a shade of truth to what Vera says. It can be hard to think of affecting any real societal change when it would be slow and gradual at best, by simply educating oneself and trying to act progressively in society, while Vera wonders how that really has anything to do with real action and sacrifice that is within one's power now.
In conclusion, I wish the actual book had been longer. There were several parts that were unpolished that I would have loved to see expanded or corrected, but I am glad to have read one 19th century female Russian author now, at least. I will certainly try to seek out more, in an effort to balance out my current exposure to Dostoevsky and others.