This book is lovely, but it is worth pointing out that it revisits characters that Levi has written in about in his previous memoirs, and is much more satisfying as an appendix than a freestanding work. The chapters on Cesare and Lorenzo gain a great deal of depth if one has already read If This Is a Man and The Truce, where the two are major characters. (These two books have unfortunately been re-titled in America, with complete inaccuracy and for mysterious reasons, Survival in Auschwitz and The Reawakening.)
Also, unlike The Periodic Table, which is also a collection of stories (and I think one of the best books of the 20th century), Moments of Reprieve is not designed to be a unified work of art. The stories were written under a variety of impulses, and most are individually brilliant and moving, but they do not gain strength from being around each other. The last chapter ("The Story of a Coin") about Rumkowski, even appears again -- with no changes as far as I could tell -- in The Drowned and the Saved, Levi's last completed book.
For anyone wanting to discover Levi's writing, I would suggest beginning with The Periodic Table, If This is a Man, and The Truce. Also wonderful are his single novel (If Not Now, When?) and his poetry. This collection, while not essential, serves as a worthy addition to his greatest work. It is also a testament to his artistry, because it shows how much he consciously left out of If This is a Man and The Truce -- stories that a lesser writer would have scrambled to include -- to create the unified, devastating impression of those two books.
Eventually, though, after reading those other great books, you will end up here, because I know of no one who has read them sincerely that has not wanted to spend more time in the company of this smart, funny, wise, and radiantly decent person.