I better answer so we can move on.
Bertrand in Lisbon, Portugal. Established in 1732.
Korn & Berg in Nürnberg opened in 1531 but was closed (destroyed) during WW2 and re-opened in 1952. So it probably would have been the oldest operating bookstore. Some parties still consider it to be the oldest.
Moravian Bookstore in Bethlehem, PA opened in 1745 would be next in line.
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