The next morning in Luzhin's rooms, he still thinks of his unfortunate break with Dunya and his thoughts are interrupted by his roommate, Lebezyatnikov, who sees himself an advanced thinker. They discuss ideas important in Russia at this time.
The discussion eventually comes around to Sonya, whom Luzhin wants to see. Luzhin insists that his roommate remain during the interview. Luzhin questions Sonya about the financial conditions of the family and about the stability of Katerina Ivanovna, who is telling people that Luzhin is going to arrange for a pension for her. Luzhin makes it clear that he has no influence, but he tells Sonya he would like to try to get some type of fund started for the widowed Katerina. To show his good intent, he gives Sonya a ten-ruble note.
Most of this chapter is a digression that allows Dostoevsky to examine some of the prominent advanced ideas of the time — ideas that were influencing such people as Raskolnikov and to a much lesser degree, the simplistic Lebezyatnikov, whom Dostoevsky depicts as an advanced liberal and a comic rube. Basically, these discussions show Dostoevsky's extreme dislike and distrust for the radical young men who are too influenced by new ideas. The foolishness of Lebezyatnikov is supposedly the foolishness of any person who adheres so closely to the "advanced ideas."
Regarding the development of the plot, this chapter merely sets up the proper machinery for Luzhin's attempt to frame Sonya.