While I can't write this essay for you, I can certainly point you in the right direction, because this book is all about suffering. The first thing I must point out to you is the genre: is an autobiography and a historical narrative.
Primo Levi was one of 650 men who was arrested in Italy during World War II. Of the 650, only three made it home after the war. Levi's thesis, which comes across very clearly in the dark poem with which he begins his account is that, at a certain level, suffering inflicted on a person by other people causes the sufferer to lose his or her humanity. This is indicative of the profound ways in which he suffered at the hands of the Nazis.
Levi's descriptions of daily life in the concentration camps will give you plenty to work with in writing your essay about suffering. Life is described as an ongoing struggle of demeaning activities in which life and death mean less than remaining human or being dehumanized.
Another great point to make in your essay is the parallels that Levi draws between life in the concentration camps and hell as it is depicted in Dante's Inferno.
This haunting autobiography provides little in the way of Levi's thoughts or feelings. It is an account of the horror that he witnessed, and the question that he wanted every reader to be left with is simply "if this is a man."
Since every essay needs a great introduction and conclusion, I would introduce the topic with a few lines about the history of the lead-up to World War II and the Holocaust. The conclusion will be where you sum up all the points that you have made.