It was Alice who went down the rabbit hole, but David Day followed her.
Day is a Canadian poet and author who did the hard work of figuring out just what Lewis Carroll was doing with Alice and all of the creatures she encountered.
The answer, in Alice's Adventures in Wonderland DECODED, is that Carroll was giving a classical education to a girl, in a way appropriate to Victorian England. So get ready; we go down the rabbit hole, too, to gain more knowledge of Carroll and his master work from David Day.