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We now get a recap of what's been going on in Kitty's social life:
She came out at the age of eighteen. (Coming out for women in the 19th Century, meant that they were socially eligible to marry.)
All the men courted her, and two were serious about it: Levin and Vronsky.
Kitty's mother doesn't approve of Levin because she doesn't understand his country ways, and thinks that he's socially awkward and has too much pride.
Kitty's father thinks that Levin is a fine match.
Kitty's mother approves strongly of Vronsky.
Vronsky, it turns out, has been very attentive to Kitty, which makes the elder Princess Shcherbatsky (Kitty's mom) hopeful of a pending engagement.
There is a slight digression into Princess Shcherbatsky's thoughts on the difficulty of marriage, since the current social climate condemns arranged marriages as old-fashioned, while complete liberty for women is not an option. The Princess is confused about the best way to marry off her last daughter.
The Princess knows that Kitty is in love with Vronsky, but is worried that Vronsky is just flirting with her.
Kitty tells her mother that Vronsky has said he never makes any important decisions without first consulting his mother, and that his mother will be arriving soon.
Kitty's mother thinks this means the decision—to marry Kitty or not to marry Kitty—may be made soon.
The Princess is further afraid that Levin will propose to Kitty and that Kitty will say yes out of some sense of honor. She tries to broach the subject with Kitty, but Kitty gets shy, and refuses to talk about it.