Alice's adventures, funny, inventive and disturbing, have fascinated and delighted children and adults alike since their publication. The fantasy worlds in which she finds herself introduce her to characters as varied and well known as the White Rabbit, the Mad Hatter, the Queen of Hearts and the Cheshire Cat...

There are at least two ways of reading this classic children's tale. One may either regard it as an innocently inventive and diverting piece for readers of all ages - or one may choose to bring to bear on it the full weight of academic analysis, be it literary, mathematical, philosophical or psychoanalytical.

The book was first published in 1865 and 1871, and has been hugely popular ever since. Unlike most Victorian children's books (including Carroll's own Sylvie and Bruno), it is refreshingly unmoralistic and brilliantly imaginative. Perhaps one might see it as a pioneering work in the rich tradition of British children's writing which includes (for example) The Wind in the Willows, the Pooh books and the animal tales of Beatrix Potter. But Alice is in many respects more demanding and disturbing - even children unaware of symbolic interpretation may well be haunted or discomfited by the dream worlds Carroll has created, worlds where it is not quite enough to say that nonsense prevails since there is almost always a kind of perverse or inverted logic at work.

In Alice's Adventures in Wonderland the child heroine dreams the experiences which constitute the story, and (of course) wakes at the end to tell her sister what has happened. The dream world of Wonderland is peopled largely by creatures which speak, feel and behave much like caricatured human beings: the White Rabbit, for instance, is clearly neurotically obsessed by time and terrified of authority, while the playing-card King and Queen of Hearts bicker like an ill-matched, long-married couple. Anger, violence and the threat of violence are real enough within the dreamworld - the dormouse is scalded and dunked at the Mad Hatter's Tea Party -while irritation and disillusionment seem more common than contentment - witness the doleful narrative of the Mock Turtle. At times, Alice seems to be in real danger, whether from flying saucepans in the Duchess' kitchen or from the attentions of a gigantic puppy, but at last she is able to break free from the suffocating power of her fantasy by exclaiming, after she has regained her normal size, 'Why, you're nothing but a pack of cards!'

Child listeners will surely be delighted by the picaresque variety of the story, but adults may wonder about some possible deeper or unifying interpretation. Freudian readings are legion, but it may be more interesting to see the adventure as a disturbing challenge to our conventional notions of reality Carroll repeatedly asks questions about the nature of time or the meaning of names, poses mathematical paradoxes and semantic quibbles - and the effect of this is to promote an acute unease, a fundamental, perhaps existential, uncertainty about meaning and purpose. Martin Gardner (editor of The Annotated Alice) suggests that 'the last level of metaphor in the Alice books is this: that life, viewed rationally and without illusion, appears to be a nonsense tale told by a mathematician.'