This is Boswell's magnum opus which has secured both his and Samuel Johnson's fame for posterity.
Boswell began work on the Life shortly after Johnson's death in 1784, but it wasn't completed until almost 7 years later.
The first edition, dedicated to Joshua Reynolds, was published in two volumes on May 16, 1791. An additional volume was published in 1794 and shortly thereafter a partly revised 2nd edition of the whole work. Boswell died in 1795, and so it was a friend of his and Johnson's - the Shakesperean scholar Edmond Malone - who edited some additional hitherto unpublished material into what is today known as the standard editions published in 1799 and 1804.
In 1831 was published a revised edition by John Croker, which was much ridiculed in a review by Thomas Macaulay. Macaulay's review is considered to have been chiefly responsible for Boswell's poor reputation from the 1830s until the discovery of his personal papers in the 1920s and 1930s. (Click here for a discussion of Boswell's reputation and Macauley's influence)
Life of Johnson is available in numerous editions, some heavily annotated, some plain paperbacks, some illustrated, some heavily edited. In recent years Yale has published the Life in their impressively annotated Research series.
An enormous number of copies in various editions ranging from very rare to cheap paperback are always available via AbeBooks.com - occassionally even 1791 first editions can be bought from there.