The linking of stories to eponymous elements is in a few cases purely metaphorical — in the opening piece the inertness of Argon represents characteristics of his ancestors, Sephardic Jews in Savoy. Levi worked as a chemist, however, and a thread running through the books is what it is to be a chemist, to wrestle with matter; the connection of the stories with elements is usually quite immediate, though sometimes circumstantial rather than substantial.
"Potassium" and "Hydrogen" centre on experiments Levi did as a student, "Nickel" on work at a nickel mine, and "Phosphorus" on a near-romance with a laboratory co-worker in wartime Milan. "Cerium" is about stealing cerium while in Auschwitz, to sell for use in cigarette lighters, and "Vanadium" about a post-war encounter with one of the German scientists encountered while working there as a slave. "Arsenic", "Nitrogen", and "Tin" are about adventures as a free-lance chemical consultant and "Chromium" and "Silver" are industrial detective stories, in which chemical problems are solved. And "Carbon" follows a carbon atom around the planet.
Rather than trying to describe how good Levi's writing is, I'll just give a sample. Here's a paragraph from the conclusion of "Nickel":
"And yet this story does not end here. Despite the many years that have passed, the liberalization of exchanges, and the fall in the international price of nickel, the news of the enormous wealth that lies in that valley in the form of rubble accessible to everyone still sets fire to the imagination. Not far from the mine, in cellars, stables, on the borderline between chemistry and white magic, there are still people who go at night to the rubble heaps and come back with bags of gray gravel, grind it, cook it, treat it with ever new reagents. The fascination of buried wealth, of two kilos of a noble silvery metal bound to a thousand kilos of sterile stone which is thrown away, has not yet died out."The Periodic Table is a delightfully original work. This elegant Everyman's Library edition comes with a brief introduction by Neal Ascherson and a chronology of Levi's life, which help place the stories in context for those coming to Primo Levi for the first time.