The First Fifteen Lives of Harry August is an entertaining time-travel meets Dr. Faustus suspense novel. It seems that time-travel novels about characters who either live their lives backward (e.g. Martin Amis' Time's Arrow ) or live them over and over again have a literary step-up on the more usual get in the machine and see the Morlocks story. I think this is because it is easier to draw parallels to our own short lives, and so enable finer literature in the former. As good as this novel is, these parallels are mostly hinted at, and the presence of the usually unmentioned time-travel paradoxes is a mild distraction.
Still, I recommend it, and it is better than many others in this sub-genre of science fiction.
Paradoxes that come to mind are: If your life is lived over and over again, is there a first time? What is special about the first time, i.e. does reality have a single time course and you are altering it over and over? If you are alive, and another kalachakra who was born before you is killed before they can be born, how will you experience it? Since so many dependent things will suddenly change in the part of your life that you have already lived, might you even suddenly cease to exist?