Alice's Adventures in Wonderland (commonly shortened to Alice in Wonderland) is an 1865 novel written by English author Charles Lutwidge Dodgson under the pseudonym Lewis Carroll. It tells of a girl named Alice who falls down a rabbit hole into a fantasy world populated by peculiar, anthropomorphic creatures. The tale plays with logic, giving the story lasting popularity with adults as well as with children. It is considered to be one of the best examples of the literary nonsense genre. Its narrative course and structure, characters and imagery have been enormously influential in both popular culture and literature, especially in the fantasy genre.

Background
Alice was published in 1865, three years after the Reverend Charles Lutwidge Dodgson and the Reverend Robinson Duckworth rowed in a boat, on 4 July 1862 (this popular date of the "golden afternoon" might be a confusion or even another Alice-tale, for that particular day was cool, cloudy and rainy), up the Isis with the three young daughters of Henry Liddell (the Vice-Chancellor of Oxford University and Dean of Christ Church): Lorina Charlotte Liddell (aged 13, born 1849) ("Prima" in the book's prefatory verse); Alice Pleasance Liddell (aged 10, born 1852) ("Secunda" in the prefatory verse); Edith Mary Liddell (aged 8, born 1853) ("Tertia" in the prefatory verse).

The journey began at Folly Bridge near Oxford and ended five miles away in the village of Godstow. During the trip the Reverend Dodgson told the girls a story that featured a bored little girl named Alice who goes looking for an adventure. The girls loved it, and Alice Liddell asked Dodgson to write it down for her. He began writing the manuscript of the story the next day, although that earliest version no longer exists. 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 for the animals presented in the book, and then had the book examined by other children—particularly the children of George MacDonald. He added his own illustrations but approached John Tenniel to illustrate the book for publication, telling him that the story had been well liked by children.

On 26 November 1864 he 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 there was an earlier version that was destroyed later by Dodgson when he wrote a more elaborate copy by hand.

But 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.

Characters
Alice
The White Rabbit
The Mouse
The Dodo
The Lory
The Eaglet
The Duck
Pat
Bill the Lizard
Puppy
The Caterpillar
The Duchess
The Cheshire Cat
The March Hare
The Hatter
The Dormouse
The Queen of Hearts
The Knave of Hearts
The King of Hearts
The Gryphon
The Mock Turtle

Character allusions
In The Annotated Alice, Martin Gardner provides background information for the characters. The members of the boating party that first heard Carroll's tale show up in Chapter 3 ("A Caucus-Race and a Long Tale"). Alice Liddell herself is there, while Carroll is caricatured as the Dodo (because Dodgson stuttered when he spoke, he sometimes pronounced his last name as Dodo-Dodgson). The Duck refers to Canon Duckworth, and the Lory and Eaglet to Alice Liddell's sisters Lorina and Edith.

Bill the Lizard may be a play on the name of British Prime Minister Benjamin Disraeli. One of Tenniel's illustrations in Through the Looking-Glass — the 1871 sequel to Alice — depicts the character referred to as the "Man in White Paper" (whom Alice meets as a fellow passenger riding on the train with her) as a caricature of Disraeli, wearing a paper hat. The illustrations of the Lion and the Unicorn (also in Looking-Glass) also bear a striking resemblance to Tenniel's Punch illustrations of Gladstone and Disraeli.

The Hatter is most likely a reference to Theophilus Carter, a furniture dealer known in Oxford for his unorthodox inventions. Tenniel apparently drew the Hatter to resemble Carter, on a suggestion of Carroll's. The Dormouse tells a story about three little sisters named Elsie, Lacie, and Tillie. These are the Liddell sisters: Elsie is L.C. (Lorina Charlotte), Tillie is Edith (her family nickname is Matilda), and Lacie is an anagram of Alice.

The Mock Turtle speaks of a Drawling-master, "an old conger eel", who came once a week to teach "Drawling, Stretching, and Fainting in Coils". This is a reference to the art critic John Ruskin, who came once a week to the Liddell house to teach the children drawing, sketching, and painting in oils. (The children did, in fact, learn well; Alice Liddell, for one, produced a number of skilful watercolours.)

The Mock Turtle also sings "Turtle Soup". This is a parody of a song called "Star of the Evening, Beautiful Star", which was performed as a trio by Lorina, Alice and Edith Liddell for Lewis Carroll in the Liddell home during the same summer in which he first told the story of Alice's Adventures Under Ground.

Writing style and themes
Symbolism
Most of the book's adventures may have been based on and influenced by people, situations and buildings in Oxford and at Christ Church, e.g., the "Rabbit Hole," which symbolised the actual stairs in the back of the main hall in Christ Church. A carving of a griffon and rabbit, as seen in Ripon Cathedral, where Carroll's father was a canon, may have provided inspiration for the tale.

Since Carroll was a mathematician at Christ Church, it has been suggested that there are many references and mathematical concepts in both this story and Through the Looking-Glass; examples include:
In chapter 1, "Down the Rabbit-Hole", in the midst of shrinking, Alice waxes philosophic concerning what final size she will end up as, perhaps "going out altogether, like a candle"; this pondering reflects the concept of a limit.
In chapter 2, "The Pool of Tears", Alice tries to perform multiplication but produces some odd results: "Let me see: four times five is twelve, and four times six is thirteen, and four times seven is—oh dear! I shall never get to twenty at that rate!" This explores the representation of numbers using different bases and positional numeral systems: 4 × 5 = 12 in base 18 notation, 4 × 6 = 13 in base 21 notation, and 4 × 7 could be 14 in base 24 notation. Continuing this sequence, going up three bases each time, the result will continue to be less than 20 in the corresponding base notation. (After 4 x 12 = 19 in Base 39, the product would be 4 x 13 = 1A in Base 42, then 1B, 1C, 1D, and so on.)
In chapter 7, "A Mad Tea-Party", the March Hare, the Hatter, and the Dormouse give several examples in which the semantic value of a sentence A is not the same value of the converse of A (for example, "Why, you might just as well say that 'I see what I eat' is the same thing as 'I eat what I see'!"); in logic and mathematics, this is discussing an inverse relationship.
Also in chapter 7, Alice ponders what it means when the changing of seats around the circular table places them back at the beginning. This is an observation of addition on the ring of integers modulo N.
The Cheshire cat fades until it disappears entirely, leaving only its wide grin, suspended in the air, leading Alice to marvel and note that she has seen a cat without a grin, but never a grin without a cat. Deep abstraction of concepts, such as non-Euclidean geometry, abstract algebra, and the beginnings of mathematical logic, was taking over mathematics at the time Dodgson was writing. Dodgson's delineation of the relationship between cat and grin can be taken to represent the very concept of mathematics and number itself. For example, instead of considering two or three apples, one may easily consider the concept of 'apple', upon which the concepts of 'two' and 'three' may seem to depend. A far more sophisticated jump is to consider the concepts of 'two' and 'three' by themselves, just like a grin, originally seemingly dependent on the cat, separated conceptually from its physical object.

Literary scholar Melanie Bayley asserted in the magazine New Scientist that Dodgson wrote Alice in Wonderland in its final form as a scathing satire on new modern mathematics that were emerging in the mid-19th century.

It has been suggested by several people, including Martin Gardner and Selwyn Goodacre, that Dodgson had an interest in the French language, choosing to make references and puns about it in the story. It is most likely that these are references to French lessons—a common feature of a Victorian middle-class girl's upbringing. For example, in the second chapter Alice posits that the mouse may be French. She therefore chooses to speak the first sentence of her French lesson-book to it: "Où est ma chatte?" ("Where is my cat?"). In Henri Bue's French translation, Alice posits that the mouse may be Italian and speaks Italian to it.

Pat's "Digging for apples" could be a cross-language pun, as pomme de terre (literally; "apple of the earth") means potato and pomme means apple, which little English girls studying French would easily guess.

In the second chapter, Alice initially addresses the mouse as "O Mouse", based on her memory of the noun declensions "in her brother's Latin Grammar, 'A mouse – of a mouse – to a mouse – a mouse – O mouse!'" These words correspond to the first five of Latin's six cases, in a traditional order established by medieval grammarians: mus (nominative), muris (genitive), muri (dative), murem (accusative), (O) mus (vocative). The sixth case, mure (ablative) is absent from Alice's recitation.

In the eighth chapter, three cards are painting the roses on a rose tree red, because they had accidentally planted a white-rose tree that The Queen of Hearts hates. Red roses symbolised the English House of Lancaster, while white roses were the symbol for their rival House of York. This scene is an allusion to the Wars of the Roses.