About the book "Through the Looking Glass and what Alice found there"
he creation of the story
In the six years since he wrote Alice in Wonderland, Charles Dodgson had been teaching Alice the mysteries of the game of chess. He had made up stories to illustrate the moves of the pieces and the rules of the game. When he came to consider a sequel, therefore, he had plenty of ideas, and had only to make up his mind as to the best way to turn his many stories into one.
In the beginning of the book, he identified the main characters with the chessmen and provided a diagram with the pieces set out for the problem which was to be solved. The chess problem is quite correctly worked out in the course of the story.
When Dodgson was in London, he met a
little girl, Alice Raikes. He invited her indoors, put an orange in her right
hand and asked her in which hand she was holding it. Then, he put her in front
of a mirror, and asked which hand the child in the mirror was holding the orange
in. Alice told him that it was in her left hand. When he asked her for
an explanation, she answered: "Supposing I was on the other side of the
glass, wouldn't the orange still be in my right hand?" He was delighted
with her answer and decided that his new book would be about the world on the
other side of the looking glass.
(source: Graham, E., Lewis Carroll and the writing of Through the Looking Glass, as an introduction in a Penguin edition of the stories)
Dodgson wanted to secure an illustrator well before the text was complete. John Tenniel was willing, but engaged with other projects. Dodgson approached Sir Joseph Noël Paton, but he was ill. Then he wrote to Tenniel, offering to buy his time from his publishers; Tenniel agreed to illustrate the book in his spare time.
The working title of Alice's new adventures was 'Looking-Glass House'. It evolved to 'Behind the Looking-Glass', but eventually Henry Liddon suggested 'Through the Looking-Glass' and the subtitle 'And What Alice Found There' was added.
(source: Stoffell, S. Lovett, Lewis Carroll in Wonderland. The life and times of Alice and her creator, 1997, p.94-95)
This sequel, "Through the Looking Glass and what Alice found there", was published in December 1871 (but was dated 1872). Tenniel's illustration of the Jabberwock was originally intended as the book's frontispiece, but it turned out to be so horrible that Carroll replaced it with the picture of the White Knight on horseback.
The wrong-way-round idea dominates the book, because this kind of game was a favourite of Dodgsons. He liked to write letters in mirror-writing, drew pictures which changed into different ones when held upside down, and he also liked to play his musical boxes backwards. Some people think that this has something to do with his left-handedness, and the asymmetry of his body.