Part I involves an unnamed rather crazed and unreliable narrator (generally known as "the Underground Man") raving and rambling against life, the universe, and everything. A few times, he rails at the scientifically established fact that free will is an illusion (because everything follows mathematically from initial conditions) and that responsibility thus does not exist. In particular, the Underground Man particular tries to think through the consequences of the eventual discovery of the ultimate formulas that describe all forthcoming human action.

Part II is the actual story, regarding the sequence of events that made the Underground Man the man he is today. His narration is still unreliable, but is primarily concerned with the events in question (and no mathematics).

An unidentified translation is online at http://eserver.org/books/dostoevsky-underground/ Mathematically minded passages are in part I, sections VII and VIII of the above. (Unfortunately, various translations differ in regard to the subdivisions, and even the paragraphing, so it's not possible to give absolute references.)