The middle child, Alice, was so taken with Dodgson's inventions – food and drink that made you shrink and grow, mythical and magical creatures, and packs of cards that came to life – that she asked him to write the story down for her. In 1864, Dodgson presented Alice with a handwritten copy entitled Alice's Adventures under Ground, which he had copiously illustrated himself.

In 1865, after adding two new episodes featuring the Cheshire Cat and the Mad Hatter, and with black-and-white illustrations by Punch cartoonist John Tenniel, Alice's Adventures in Wonderland was published, with Dodgson using the pseudonym "Lewis Carroll", based on the Latin forms of his Christian names.

One hundred and fifty years later, Carroll's "little dream-child" and her companions have become a part of our cultural fabric. Alice's Adventures in Wonderland has never been out of print, captivating generations of readers, child and adult alike. It has also apparently been translated into more languages than any other book except The Bible. One wonders if it would have had quite the same appeal if the editor had accepted one of Dodgson's original suggestion that it be called Alice among the Fairies and that his nom de plume be "Edgar Cuthwellis".

One of the reasons for the success of this brilliant example of literary nonsense is that Carroll's main aim was to delight children rather than to educate them. The book is awash with parodies of well-meaning cautionary verses, and the usually self-deprecating Carroll thumbs his nose at the moralising tone which was common in books for children at the time. His over-the-top characters,  from the nervy White Rabbit, to the bombastic Queen of Hearts and the hyperactive Mad Hatter,  are all fantastically realised inventions of an obviously clever and creative mind.

The 150th anniversary is spurning a plethora of versions of this much-loved children's book, including the impressive The Complete Alice, published by Macmillan, the original publishers. From its elegantly embossed white front cover, to the shiny miniature hearts above the page numbers and the hand-coloured reproductions of John Tenniel's illustrations, this is a beautiful and highly collectable tome.

As the title suggests, it contains both Alice's Adventures in Wonderland and the sequel Through the Looking Glass and What Alice Found There, which was originally published in 1872. The Complete Alice also includes an introduction by Philip Pullman, author of the fantasy series His Dark Materials, along with a selection of letters and introductory pieces written by Carroll for earlier editions. Also featured are plates and vignettes of Tenniel's illustrations, coloured by Diz Wallis and Harry Theaker.

I still have my cherished first copy of Alice, a novel-sized version with an uninspiring green cover and small black-and-white illustrations at the beginning of each chapter. It was given to me for my eighth birthday by my great-grandmother, a formidable woman whose inscription – containing just my full name, the date and the words "from Nanny Owen" – probably reflects the formality of the 1950s.

It is one of my favourite children's books, and its condition attests to years of love and multiple readings, with tape holding it together and many words underlined in pencil so I could look them up in the dictionary later, without ruining the flow of the storytelling process.

These days, I collect illustrated versions of Alice, fascinated by the way in which different illustrators have interpreted much-loved characters such as the Cheshire Cat, the White Rabbit, the Mad Hatter and, of course, Alice herself. One of the earliest versions is by Arthur Rackham, renowned for his illustrations of classics such as Peter Pan in Kensington Gardens. His Alice has a pretty, ethereal quality.

Tove Jansson, author-illustrator of the much-loved Moomin books, has created a more down-to-earth Alice and introduced a troll-like cheekiness to many of the other characters. Multi-award-winning English illustrator Anthony Browne has conjured up a somewhat suburban Alice, dressed in dowdy green, while his compatriot, Helen Oxenbury, has produced a sassy, modern Alice, who wears a blue shift-dress and has long, unkempt flyaway hair. Her body language shows that she is never intimidated, even by the blustering Queen of Hearts with her constant cries of "Off with their heads".

Australian illustrators have also turned their hand to these iconic images, including Robert Ingpen, winner of the Hans Christian Andersen Medal for Illustration in 1986, with a charming auburn-haired, long-limbed Alice. There is also an Aboriginal version, titled Alitji in Dreamland, in which a sinuous naked Alice wafts through highly coloured and textured dream landscapes inhabited by Australian native animal versions of Carroll's characters.

Artists have also been drawn to this classic tale, including surrealist Salvador Dali in 1969. His stylised silhouette Alice floats through a fittingly psychedelic interpretative landscape. But it is invariably John Tenniel's original illustrations, with his contemplative and beautifully drawn Alice, that most people see in their mind's eye when they think of Alice and her adventures.

The book has also inspired some modern children's classics, including The Wonderful Wizard of Oz by Frank Baum, Ethel Pedley's Dot and the Kangaroo and Norton Juster's highly imaginative The Phantom Tollbooth. It has been reinterpreted for stage, television and film, including a silent film in 1903, the classic animated Disney version in 1951, and Tim Burton's darkly exuberant 2010 film, starring Canberra's own Mia Wasikowska as Alice and the inimitable Johnny Depp as the Mad Hatter. No doubt there will be more.

So perhaps now is the perfect time to revisit this classic children's book, sing a verse or two of Twinkle Twinkle Little Bat or recite Jabberwocky, and help celebrate the wonderfully wacky, nonsensical, joyous world created by the sometimes controversial but ultimately enduring Lewis Carroll.

Stephanie Owen Reeder is an award-winning Canberra reviewer, author and editor, whose latest book is Lennie the Legend: Solo to Sydney by Pony (NLA Publishing).

The Complete Alice, by Lewis Carroll. (MacMillan, $54.99.)