The Periodic Table is a collection of short stories, some autobiographical, some not, each one associated in some way with a different chemical element. You might think that this would appear contrived, but it doesn't because Primo Levi weaves most of the stories around his day-to-day life as an industrial chemist in Italy before, during, and after the Second World War. The impact of Fascism runs as a theme through many of the stories, although only one is directly about Levi's experiences in Auschwitz. The translation from the Italian by Raymond Rosenthal is smooth and unobtrusive. The stories are varied and stimulating and I found I could read three or four of them at a sitting without my interest flagging.
Should students of chemistry read this book? Well, yes, I think they should, but not for the little bit of chemistry they might pick up from it, but because it is a good read and it is part of the cultural heritage of their subject (in the same way that The Double Helix by James Watson is for molecular biology).