Alice in Wonderland got its start as a simple story, told by a mathematics professor to a colleague's daughter. It's a strange story that seems to be the result of a drug trip, but is actually a scathing satire of the new-fangled math that the professor was seeing invade his area of study. There are many different guides to the math of Alice in Wonderland. Here are some great sites that you can get for free, that you can read to get a better understanding of Alice in Wonderland. Or read as a class to gain math insight from students in the class.
There are other great books out there that may more fully describe each mathematical encounter Lewis Carrol came in contact with during the book Alice in Wonderland.