The Doctor's Dilemma

 was a book written by George Bernard Shaw and published by Penguin Books.

The Doctor added the book to his collection at least by his seventh incarnation, reading through it while he and Mel were seated at a table in Anderson's ice cream parlour in Iceworld. (TV: Dragonfire)

Trix once woke up while the TARDIS was in flight and caught the Eighth Doctor reading it. When called on it, the Doctor then launched into a brief account of how he'd bet Shaw at a party hosted by Oscar Wilde. (PROSE: The Gallifrey Chronicles)

Behind the scenes

 * The appearance of the book in Dragonfire was part of a larger running gag developed by Sylvester McCoy wherein, each time the Doctor pulls out a book to read, it has the word "Doctor" somewhere in the title. (Source: Remembrance of the Daleks DVD audio commentary)
 * featured Colin Gordon, Terence Alexander, Peter Sallis and Mary Reynolds in supporting roles.