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Larry Niven's second collection (from 1969) had already been raided for the "Known Space" and "Gil the Arm" stories it contained by including those in newer collections with matching stories from those series. In 1979, Niven decided to revive/re-collect the remaining stories from The Shape of Space (the first 7 stories, below) and bundle them with an equal amount of newer, previously uncollected stories in this collection: Convergent Series. Five of these (#10 through 14) are from his "Draco Tavern" series - their first appearance in a Niven collection. The first few stories were originally part of his "Known Space" series but later dropped from the timeline because of inconsistencies with newer stories and novels. I'll recommend "The Deadlier Weapon" (not SF) and "Wrong Way Street."
Bordered In Black
Original appearances from 1965 to 1978 - in Magazine of F&SF (5), Galaxy (2), IF (2), Ellery Queen's, Cosmos (as "3 Vignettes"), Isaac Asimov's, Analog, Vertex, Ariel #3, Stellar 1, Stellar 2, Destinies (Nov-Dec,1978.)