These are two separate children’s books, but the edition I read is one of several in which they are bundled together. Besides the fact that each is only a little over 100 pages, they are conveniently bundled because they share the same lead character, Alice, and take place in similar (arguably the same) alternate realities: Wonderland and the Looking-Glass World. These are worlds in which strange events are common place and there’s little compulsion to behave logically– worlds in which imagination rules and reality only provides a subconscious shaping of events.
In the former book, Alice enters the alternate world by tumbling down the rabbit hole and in the later she does so by stepping through a mirror (i.e. a looking-glass.) Each of these books follows Alice from her entry into the alternate reality, through a series of adventures, and then back to the real world.
Not much of a review is necessary because even though—given you are reading a review—you probably haven’t read the books yet, you will be familiar with many of the characters and references from widespread appearance in pop culture. I already mentioned the tumble down the rabbit hole, as does Morpheus (Laurence Fishburne) in “The Matrix.” That movie also references chasing the white rabbit, as does a famous song by Grace Slick. You’ve also probably seen or heard references to the grin of the Cheshire Cat and the frenetic behavior of the Mad Hatter. “Through the Looking-Glass” features several well-known characters from English nursery rhymes (e.g. Tweedledee & Tweedledum as well as Humpty Dumpty.)
It’s also not so important to get into plot because the stories are purposefully chaotic and exist in a world of loose logic. The strings of causality are not so strong, but it’s on purpose. It’s supposed to be a strange and surreal world, and it achieves great success in this regard. Events don’t have to make sense; they just have to be imaginable. This doesn’t mean that there is no flow or transitions between the adventures in these books. There is. It’s more easily recognized in “Through the Looking-Glass” in which a game of chess provides an underlying structure for the unfolding of events.
I’d recommend everybody read these books. While I referred to them as “children’s books,” I also agree with Neil Gaiman’s point that that is a nonsense term. So one shouldn’t think one missed the boat and there is no going back.