The next day, Oblonsky goes to a ballet rehearsal to see his current mistress, a ballet dancer.
Afterward, he goes to the marketplace to select produce for dinner, and then he stops by Dussot's, where he plans on seeing three people: Levin, who has returned from his trip abroad, the new head of his department, and Karenin, who he wants to ensure will be coming for dinner.
The guest list for dinner is: Kitty, Levin, a girl cousin, young Shcherbatsky, Koznyshev, Karenin, and Pestsov. Oblonsky considers Koznyshev and Karenin to be the main course of the guests, and Pestsov to be an interesting garnish. (Pestsov is a liberal intellectual who also likes music and history.)
Oblonsky's happiness is marred by only two unpleasant circumstances. The first is that, judging from Karenin's chilliness towards Oblonsky, things are not going well between Karenin and Anna (who is, of course, Oblonsky's sister). The second problem is that Oblonsky's new department head has a strong work ethic and different opinions from Oblonsky. We have a feeling Oblonsky is more worried about the former than the latter.
Oblonsky first has a brief chat with Levin, who won't stop talking about workers and inequality. Levin has visited Germany, Prussia, France and England, and has determined that there is no "worker problem" in Russia (such as we might hear of in Marxist or socialist philosophies of the time; check out "What Is Marxism?").
Instead, what is causing the Russian peasants to fall behind is that their natural relationship to the land is being interrupted and destroyed. (Muzhiks aren't the same as Western European factory laborers, after all). Levin has also learned some humility, though. He acknowledges that this world we live in is profoundly insignificant, and that we all seek pleasures because we are trying to avoid thinking about death.
Oblonsky only hears the "pleasures" comment, and says that Levin's finally starting to agree with Oblonsky's own way of living his life.
Levin promises to come to dinner. Not surprisingly, Levin is too shy to ask if Kitty will be there.
Oblonsky then goes in to see his new department head, who turns out to be friendly. They chat until four o'clock, at which point Oblonsky realizes that he still needs to see Karenin.