Through the Looking-Glass, and What Alice Found There (also known as Alice Through the Looking-Glass or simply Through the Looking-Glass) is a novel published on 27 December 1871 (though indicated as 1872) by Lewis Carroll and the sequel to Alice's Adventures in Wonderland (1865). Alice again enters a fantastical world, this time by climbing through a mirror into the world that she can see beyond it. There she finds that, just like a reflection, everything is reversed, including logic (for example, running helps you remain stationary, walking away from something brings you towards it, chessmen are alive, nursery rhyme characters exist, and so on).
If you read Alice's Adventures in Wonderland and thought there was a bunch missing, you'll find much of what you're looking for here. Again, charming and classic, though with even more fanciful imagination.