This group of nine anthologies compiles winners of the Hugo Awards in the short fiction categories, each book covering three or more years. The first volume was Isaac Asimov's first anthology. He explains in the introduction to the later 1989 volume that the idea was Avram Davidson's, who had won a short story Hugo, and Asimov was asked to be editor as a prominent author who had not (yet) won a Hugo.

The contents of each book were pre-selected, of course; Asimov's editorial contributions were the long chatty introduction and story headnotes, typically anecdotes about how Asimov met the author, or reminiscences of the author's earlier landmark stories that had impressed Asimov. (Longish personal story notes and afterwords came to characterize Asimov's subsequent collections and anthologies, like The Early Asimov and Before the Golden Age, and perhaps inspired Harlan Ellison's even more extravagent introductions to the stories in Dangerous Visions.)

Asimov left off the individual story introductions in the last volume he "presented," published just a year before his death. Martin H. Greenberg, who'd been doing the editorial chores for Asimov's anthologies for over a decade, put together two final volumes, "presented" and with story introductions by Connie Willis and then Gregory Benford.

(One later Hugo anthology was published in 2010 by Mary Robinette Kowal, The Hugo Award Showcase: 2010 Volume [isfdb] with both winners and some nominees from the previous year's awards.)

The combined contents below are nothing more nor less than all the Hugo winning short fiction published up to 1993. Both Poul Anderson and Harlan Ellison are here 7 times; Fritz Leiber, Larry Niven, Connie Willis, and Roger Zelazny, 4 times each.