He began writing the manuscript of the story the next day, although that earliest version is lost to history.
The girls and Dodgson took another boat trip a month later when he elaborated the plot to the story of Alice, and in November he began working on the manuscript in earnest.

To add the finishing touches he researched natural history in connection with the animals presented in the book, and then had the book examined by other children — particularly those of George MacDonald.
Though Dodgson did add his own illustrations, he subsequently approached John Tenniel to illustrate the book for publication, telling him that the story had been well liked by children.

On 26 November 1864, Dodgson gave Alice the handwritten manuscript of Alice's Adventures Under Ground, with illustrations by Dodgson himself, dedicating it as "A Christmas Gift to a Dear Child in Memory of a Summer's Day".
Some, including Martin Gardner, speculate that there was an earlier version that was  destroyed later by Dodgson when he wrote a more elaborate copy by hand.

Before Alice received her copy, Dodgson was already preparing it for publication and expanding the 15,500-word original to 27,500 words, most notably adding the episodes about the Cheshire Cat and the Mad Tea Party.
He began writing the manuscript of the story the next day, although that earliest version is lost to history. The girls and Dodgson took another boat trip a month later when he elaborated the plot to the story of Alice, and in November he began working on the manuscript in earnest.
To add the finishing touches he researched natural history in connection with the animals presented in the book, and then had the book examined by other children — particularly those of George MacDonald. Though Dodgson did add his own illustrations, he subsequently approached John Tenniel to illustrate the book for publication, telling him that the story had been well liked by children.
On 26 November 1864, Dodgson gave Alice the handwritten manuscript of Alice's Adventures Under Ground, with illustrations by Dodgson himself, dedicating it as "A Christmas Gift to a Dear Child in Memory of a Summer's Day". Some, including Martin Gardner, speculate that there was an earlier version that was  destroyed later by Dodgson when he wrote a more elaborate copy by hand.
Before Alice received her copy, Dodgson was already preparing it for publication and expanding the 15,500-word original to 27,500 words, most notably adding the episodes about the Cheshire Cat and the Mad Tea Party.
Alice's Adventures in Wonderland