The Periodic Table, by Primo Levi, consists of twenty-one short stories, each of which has the name of a different element as its title. The stories generally deal with topics including Levi’s life as a chemist and his experiences in the Holocaust and World War II. As a result, many of the relevant quotes from the book are about these topics.
The following quotes have been translated from the original language of the book (Italian), so Levi did not actually write these quotes in English.
For example, a good quote about Levi’s philosophy is this one:
Perfection belongs to narrated events, not to those we live.
The experiences that Levi went through were nothing if not messy. He had to steal Cerium in order to sell it while at a concentration camp for survival, for example.
Another quote relevant to stories like the Cerium one is as follows:
Our ignorance allowed us to live, as you are in the mountains, and your rope is frayed and about to break, but you don’t know it and feel safe.
This speaks to the experience of living through the Holocaust, since many people didn’t know the severity of what was about to happen beforehand.
All in all, maybe the best quote from Levi's point of view to sum up the book is this one:
The nobility of man, acquired in a hundred centuries of trial and error, lay in making himself the conqueror of matter.