Alice's Adventures in Wonderland: complexity beneath a cheerful surface

Nonsense at its best, speaking animals, and curious adventures: Alice's Adventures in Wonderland by Lewis Carroll is definetively an enjoyment. Children will love the episodes about the little girl's wonderful adventures, her encounters with weird creatures. Additionally, the stories are written in a light-hearted, easy-to-read way.
But adults can also take delight in this novel - and even more. One of the novel's major strength is its pun. There is the literal level of language, where metaphors simply do not work, such as

"one of the guinea-pigs (...) was suppressed(...). (As that is rather a hard word, I will just explain to you how it was done. They had a large canvas bag, which tied up at the mouth with strings: into this they slipped the guinea-pig, head first, and then sat upon it.) "I'm glad I've seen that done" thought Alice. "I've so often read in the newspaper, at the end of trials, 'There was some attempt at applause, which was immediately suppressed by the officers of the court,' and I never understood what it meant till now.""

Or the confusion caused by the misunderstanding of (almost) similiar pronounced words:

"'Mine is a long and sad tale!' said the Mouse.(...) 'It is a long tail, certainly,' said Alice, looking down with wonder at the Mouse's tail; ' but why do you call it sad?'"

These are just two examples to get a first impression, there is much more in the text, and some passages really make you smile.
But beneath this funny surface - though it might lead to question the meaning and importance of language - are more serious topics, such as the lost of childish innocence and Alice's struggle to define and form her identity as she constantly changes her size. "Who in the world I am?" is one of the central questions in this novel. I do not want to give away too much of the stories, just be prepared that there is a lot going on. Alice's Adventure's in Wonderland is not only a happy fairy-tale.
So, is this novel a good novel to educate your children? That is a question depending on your understanding of education. Alice sometimes seems to be a well-schooled girl, but she is also noisy, saucy, impertinent and precocious. If you want a well-behaved child who simply memorizes his/her lessons, than I recommend not to use this novel as a mean of education. Carroll rather emphasizes a very modern understanding of learning and education, comparable to Kingsley's understanding presented in his novel Water Babies, published a couple of years ago: learning through experience. If you want a self-cofident child that will be able to deal with unexpected, extraordinary situations (after a while), to progress by learning/experiencing, that is able to speak for itself, to make own decisions (to certain degrees), than you can use this novel as an educational one, but be aware that Alice does not always serve as a role model.
No matter how you approach this novel, the reading will be enriching. Even if you do not like (to think of) the existential questions, you will have some cheerful hours at least.