She researches Isaac Babel and helps organise a Babel conference in California, attends a Tolstoy conference held in Tolstoy's house, briefly works on a Turkish travel guide, does a study abroad stint in Moscow, spends several months in Samarkand studying Uzbek language and literature, goes to St Petersburg to write a piece on a reconstruction of Empress Anna's ice palace, and visits Florence. These travel anecdotes are mixed up with details of her student and academic life, deciding to study literary theory and comparative literature rather than creative writing, applying for strange grants, meeting idiosyncratic and esoteric academics, and so forth.
All of this is leavened by a variety of literary anecdotes, touching on Babel's civil war experiences and his murder by Stalin, the dramatic family conflicts of Tolstoy's final years, the lives of Navoi and other Uzbek writers, and so forth. And a tiny amount of literary theory is thrown into the mix.
The final chapter — actually a stand-alone essay — carries the same title as the book and is fairly representative. Batuman starts with a brief visit of her own to Florence, which leads via Dostoyevksy's experiences there to a summary and analysis of his novel The Demons. This is followed by a description of the circle of graduate students Batuman was part of and an account of their lives, which is linked back to The Demons by psychological parallels and the critical theory of René Girard.
This is all pitched at the level of popular literary magazines, and indeed various bits of it have previously appeared in the New Yorker and Harper's Magazine. So you don't need to have read any of the writers Batuman discusses or know any literary theory to appreciate it.
We never escape Batuman's presence in The Possessed, so how you feel about it will depend on how well you get on with her. I found her pleasant company for a few hours of easy reading, but I can imagine some people finding her irritating — perhaps her fondness for finding meaning in apparently trivial events will be annoying — in which case it won't go down so well.