Being grown up
When Carroll wrote Through the Looking Glass, the real Alice had already become a grown woman. In the introductory poem, he recalls the glorious days of her childhood, and we notice his sadness because his favorite child-friend has grown up, got married, and does not contact him anymore.
In the first book, Alice was very bewildered by the crazy adult world. In Through the Looking Glass, however, we see that Alice has grown up, as well as the real Alice has, and that she is more confident with herself when associating with the Wonderland characters. While she was being lectured and ordered about in the first story, she now teaches some of the Wonderland characters a lesson and even mothers them, like she does with the clumsy White Knight.
Learning to achieve a higher social position
However, there are still things to learn. Alice’s wish (and motive) in Through the Looking Glass is becoming a queen. To achieve this, she has to adhere to the rules of a chess game. She has to reach the final square, and can interact only with creatures that are on a square directly next to hers.
She also has to learn more about the way things are. For example, the flowers tell her that they are lower in social rank than she is (“it isn’t manners for us to begin, you know”), she learns about the tragic lives of the lower class (Bread-and-Butterflies always die because of a food shortage), and Tweedledee and Tweedledum teach her some more social skills.
In fact, Alice is trying to reach a higher social position, and she has to master certain rules of behavior that come with this social order.
In the sequel, the concept of identity is touched upon again. Although Alice is more sure of herself, her identity is again questioned. When she enters the wood, she promptly forgets her own name. The fawn does not even recognize her as a human being.
But this time the question of identity is lifted to an even higher level: Tweedledee and Tweedledum show Alice the sleeping Red King and tell her that she is not a real person; she only exists in his dream. At first Alice does not want to believe that she ceases to exist when the King wakes up. But at the end of the book, the matter is still not resolved: