Perthshire-born Robertson’s The Long Take, a novel told in verse, was desribed by the judges as a “film noir on the page”.
A Fellow of the Royal Society of Literature, Robertson has published five collections of poetry and has received a number of honours.
Read our review of The Long Take here
A graphic novel has also been included on the longlist for the first time.
Sabrina, by the American author Nick Drnaso, employs deliberately simplistic drawings to illustrate its story of violence and “fake news” conspiracy theories.
The Man Booker judges, headed by the philosopher Kwame Anthony Appiah, said: “Given the changing shape of fiction, it was only a matter of time before a graphic novel was included on the Man Booker longlist. Sabrina makes demands on the reader in precisely the way all good fiction does.”
The past two winners of the £50,000 award have been American.