This is a Book, By Demetri Martin

With the Edinburgh Festival Fringe only three weeks away, what better aperitif for the comedy lover than a book by one of the festival's champions?

The hipster US stand-up/actor/ musician/sketcher, Demetri Martin, won the Perrier Award for his show If I in 2003, and has gone on to write for Late Night with Conan O'Brien and Jon Stewart's irreverent The Daily Show, as well as two series of his own Important Things with Demetri Martin.

Martin's stand-up comedy mixes pithy stories, abstract observations, lengthy palindromes, and sketches drawn on oversized flipcharts that provide either the set-up or punchline to a gag. These add a visual exclamation mark that counterpoises Martin's bone-dry, understated delivery.

So how does it translate to the page? Much like the acts at the Fringe, This is a Book is quite the miscellany. Oddly, given that a book is a more obvious setting for illustrations than a stage, Martin's drawings lack punch in print. There is the odd zinger – "Superhero (just lying down)", for instance, whose title wilfully undercuts the image of a hero apparently in full flight – but, in the main, they are more like bad greeting-card puns than clever witticisms. Yet it is easy enough to flip through the sketches – taking them for the quick-hit sideshow that they are – and move on to the writing.

To give a brief preview of the type of absurd, surrealist riffs on offer, there is: a conceptual melodrama based around a "protagonists' hospital", where the doctors grow tired of treating tanned, stubbled patients carted in with oddly non-life-threatening bullet wounds; an essay on what it's like to be raised by a man raised by wolves ("Dad hated fairy tales. If you even mentioned one to him, he'd launch into one of his long, self-righteous speeches about the damage done to the wolf community by the 'prey-biased fairy-tale media'"); and aliens who demand to talk to Earth's one and only ruler: Miss Universe.

All are fun flights of fancy, nicely explored in short form, but the book really comes alive during the longer pieces. One, concerning a man's relationship with a ghost after a near-death experience, is cleverly plotted, beautifully broken-hearted in tone and nicely paced, while Martin's breakdown of the "missing chapter" from Dickens's A Christmas Carol – the appearance of the Ghost of Christmas Future Perfect – delightfully plays with the confusion that anyone who has studied grammar will recognise.

When it comes to his quick-hit one-liner "statistics", several are less than hilarious, but Martin's deftness with language is obvious in an extraordinary, three-page, palindromic poem, and excerpts from his "often-true autobiography" as delicious as: "We started to see less and less of each other. And that's when I knew it was quicksand."

This is a Book is a diverse grab-bag, then, but it is clear that this is a comedian who puts real thought into the words he uses – and, as such, there is plenty that bears repeat reading.