The narration by the Underground Man is laden with ideological allusions and complex conversations regarding the political climate of the time period. Using his fiction as a weapon of ideological discourse, Dostoevsky challenges the ideologies of his time, mainly nihilism and rational egoism. In Part 2, the rant the Underground Man unloads on Liza as they sit in the dark is a moment in which such a discussion of clashing ideologies occurs. Liza believes she can survive and rise up through the ranks of her brothel as a means of achieving her dreams of functioning successfully in society. However, as the Underground Man points out in his rant, such dreams are based on a utopian trust of not only the societal systems in place but also humanity's ability to avoid corruption and irrationality in general. The points made in Part 1 about the Underground Man's pleasure in being rude and refusing to seek medical help are his examples of how idealised rationality is inherently flawed for not accounting for the darker and more irrational side of humanity. The Underground Man argues that underlying the gilded understanding of society is what he tells Liza will end up leading her down a calamitous path and ultimately destroy her.
Where the Underground Man places himself in this messy view of society is rather complicated. He is very open about his irrational and spiteful interaction with the world, but he also admits that he understands the pleasure in "a doll to play with" or "a cup of tea with sugar in it" (these being symbols of a non-corrupted society). The important distinction here is that the Underground Man would lie awake grinding his teeth for months after because of such an indulgence in society. The shame displayed here is what separates him from rational egoists and utopian dreamers, but the desire that he sometimes feels to buy into such ideals leaves him on the fringe of society or what can be understood as what drove him underground.
The unreliable narrator is used in the entire story. Although the novel is written in first-person narrative, the "I" is never really discovered. The novel's style is also linked to the St. Petersburg Tales in which there is an unreliable narrator. The writing style is very dense and at times difficult to understand. The sentence structure can at times seem "multi-layered"; the subject and the verb are often at the very beginning of the sentence before the object goes into the depths of the narrator's thoughts. The narrator repeats many of his concepts.
When the narrator says that he is "underground", he speaks metaphorically; he is not actually underground. Rather, in chapter 11, he refers back to his inferiority to everyone around him and describes listening to people like "listening through a crack under the floor". The word underground actually comes from a bad translation into English. A better translation would be a crawl space: a space under the floor that is not big enough for a human, but where rodents and bugs live. According to Russian folklore it is also a place where evil spirits live.
The Stone Wall is one of the symbols in the novel and represents all the barriers of the laws of nature that stand against man and his freedom. Put simply, the rule 2+2=4 angers the Underground Man because he wants the freedom to say 2+2=5, but that Stone Wall of nature's laws stands in front of him and his free will.