In his introduction Knight states that his aim was "to put together the biggest and most comprehensive collection of good science fiction that I possibly could... in my belief they are stories that will be anthologized again - and again - because they have the qualites that make for lasting pleasure... This is the kind of big meaty selection I wish someone had given me when I was a teen-aged science fiction addict in Hood River, Oregon." Looking over the contents, I agree: this is the kind of book you hand to someone just starting to be intested in SF - to hook them for sure. Another book of this sort is the 2-volume anthology A Treasury of Great Science Fiction. That was the book I encountered when starting out, but I think this one would do as well. Or better yet: both - there is no overlap between the sets. Stories are from 1931 to 1970: most are from Astounding, Galaxy, and Magazine of F&SF.

Contents:
(Introduction by Damon Knight)
BOOK 1:
"Green Thoughts" by John Collier
"The Red Queen's Race" by Isaac Asimov
"The Cure" by Henry Kuttner & C. L. Moore
"Consider Her Ways" by John Wyndham
"An Ornament to His Profession" by Charles L. Harness
"The Third Level" by Jack Finney
"One Ordinary Day, With Peanuts" by Shirley Jackson
"Bernie the Faust" by William Tenn
"Light of Other Days" by Bob Shaw
"The Game of Rat and Dragon" by Cordwainer Smith
"Becalmed in Hell" by Larry Niven
"Apology to Inky" by Robert M. Green, Jr.
The Demolished Man by Alfred Bester [the complete novel]

BOOK 2:
"Day Million" by Frederik Pohl
"Manna" by Peter Phillips
"Can You Feel Anything When I Do This?" by Robert Sheckley
"Somerset Dreams" by Kate Wilhelm
"He Walked Around the Horses" by H. Beam Piper
"Rump-Titty-Titty-Tum-Tah-Tee" by Fritz Leiber
"Sea Wrack" by Edward Jesby
"Man in His Time" by Brian W. Aldiss
"Four Brands of Impossible" by Norman Kagan
"Built Up Logically" by Howard Schoenfeld
"Judgement Day" by L. Sprague de Camp
"Journey's End" by Poul Anderson
More Than Human by Theodore Sturgeon [the complete novel]