Only 22 copies of the 1865 first edition are thought to exist, one of which is owned by the National Library of Scotland in Edinburgh.
This first edition was withdrawn after the illustrator, John Tenniel, complained about the quality of the printed illustrations.
Recipients of presentation copies were asked to return them, and only a few bound copies have survived.
Visitors will be able to see the library’s copy of the book open at the title page in a special display of rare Alice books to mark the 150th anniversary of the first publication.
The library’s rare books curator Graham Hogg said: “The story of Alice has delighted generations of children and we are very pleased to be able to show people where it all started by displaying a copy of the first ever printing of the book.”
The library’s copy of the book is in its original red cloth binding.
Another copy of the 1865 first edition, which was the author Lewis Carroll’s working copy, sold at auction in New York 17 years ago for £1 million.
Alice’s Adventures In Wonderland was written by Charles Lutwidge Dodgson under the pseudonym Lewis Carroll and quickly became a children’s classic.
Also on display in the exhibition will be two copies of the 1866 second edition of Alice, which was the first edition sold to the public.
The books will be open to show two of Tenniel’s most famous illustrations - Alice meeting the Cheshire cat and Alice at the Mad Hatter’s tea party.
Visitors will be able to view the rare works in the Library’s Boardroom this Thursday from 4.30pm until 6.30pm.
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