The Cheshire Cat is another fictional character in the novel.
The Cheshire Cat is the cat of the Duchess. Alice meets it when she leaves the Duchess' s house, and sees it in a tree. It constantly grins and can disappear and reappear whenever it likes. Sometimes it disappears and leaves its grin behind. The Cheshire Cat is the only character in Wonderland who actually listens to Alice. He teaches Alice the 'rules' of Wonderland.
The cat sometimes raises philosophical points that annoy or baffle Alice. It does, however, appear to cheer her up when sentenced to death baffles everyone by having made its head appear without its body, sparking a massive argument between the executioner and the King and Queen of Hearts about whether something that does not have a body can indeed be beheaded.
At one point, the cat disappears gradually until nothing is left but its grin, prompting Alice to remark that she has often seen a cat without a grin but never a grin without a cat.
The White Rabbit is the first character Alice encounters in Wonderland. He is mentioned in chapters 1, 2, 4, 8, 11 and 12 of “Alice’s Adventure in the Wonderland”.
Alice follows him when he hurries into his hole and thereby enters Wonderland. While walking through Wonderland, Alice comes upon his house where the White Rabbit, still in a hurry, mistakes her for his housemaid Mary Anne, and orders her to get his gloves and a fan.
When she grows and gets stuck in the house, the Rabbit orders Pat to get her out. In the end we discover that the White Rabbit is a herald in the Queen of Heart’s court. The White Rabbit is nervous and always in a hurry. However, he is confident enough about himself to contradict the King of Hearts.
Because Alice follows him, he gets things moving again whenever he appears during the story. In a way, he is some kind of a guide through Wonderland for her, only unintentionally.