One of the earliest SF anthology series, these books, published only in the UK, were of great influence, according
to The Encyclopedia of Science Fiction: "When
Best SF (anth 1955) appeared it was unique in several ways: its editor was a respected literary figure; its publisher, Faber and Faber, was a prestigious one; and it made no apologies or excuses for presenting sf as a legitimate form of writing. Moreover, Crispin's selection of stories showed him to be thoroughly familiar with sf in both magazine and book form, and his introductions to this and succeeding volumes were informed and illuminating."
Most reprinted authors: Brian W. Aldiss (5), Eric Frank Russell (4), then Ray Bradbury, Fredric Brown, and John Wyndham (3 each).
Cover scans are adapted from isfdb.
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Best SF, (Faber & Faber , 1955)
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Best SF 2, (Faber & Faber , 1956)
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Best SF 3, (Faber & Faber , 1958)
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Best SF 4, (Faber & Faber , 1961)
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Best SF 5, (Faber & Faber , 1963)
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Best SF 6, (Faber & Faber , 1967)
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Best SF 7, (Faber & Faber , 1970)
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Combined Contents by Author and Title
Brian W. Aldiss
Heresies of the Huge God
(Galaxy Aug 1966)
-- Vol. #7
Old Hundredth
(New Worlds Nov 1960)
-- Vol. #6
Outside
(New Worlds Jan 1955)
-- Vol. #2
Psyclops
(New Worlds Jul 1956)
-- Vol. #4
Who Can Replace a Man?
(Infinity Science Fiction Jun 1958)
-- Vol. #5
Poul Anderson
The Martyr
(F&SF Mar 1960)
-- Vol. #5
Christopher Anvil
The Prisoner
(Astounding Feb 1956)
-- Vol. #5
Isaac Asimov
Little Lost Robot
(Astounding Mar 1947)
-- Vol. #2
The Machine That Won the War
(F&SF Oct 1961)
-- Vol. #7
J. G. Ballard
Billennium
(New Worlds Nov 1961)
-- Vol. #6
Alfred Bester
Hobson's Choice
(F&SF Aug 1952)
-- Vol. #2
Jerome Bixby
It's a Good Life
(Star Science Fiction Stories, 1953)
-- Vol. #4
James Blish
A Case of Conscience
(If Sep 1953)
-- Vol. #1
A Work of Art
(Science Fiction Stories Jul 1956)
-- Vol. #6
Anthony Boucher
Balaam
(9 Tales of Space and Time, 1954)
-- Vol. #4
The Quest for Saint Aquin
(New Tales of Space and Time, 1951)
-- Vol. #5
Ray Bradbury
The Fire Balloons
(Imagination Apr 1951)
-- Vol. #1
Kaleidoscope
(Thrilling Wonder Stories Oct 1949)
-- Vol. #6
Zero Hour
(Planet Stories Fll 1947)
-- Vol. #2
Bill Brown
The Star Ducks
(F&SF Fll 1950)
-- Vol. #6
Fredric Brown
Answer
(Angels and Spaceships, 1954)
-- Vol. #3
Letter to a Phoenix
(Astounding Aug 1949)
-- Vol. #6
Placet Is a Crazy Place
(Astounding May 1946)
-- Vol. #2
John Brunner
Protect Me from My Friends
(F&SF Nov 1962)
-- Vol. #7
Algis Budrys
Death March
(Astounding Oct 1956)
-- Vol. #6
John Christopher
The New Wine
(Fantastic Story Magazine Sum 1954)
-- Vol. #1
Weapon
(The Twenty-Second Century, 1954)
-- Vol. #6
Arthur C. Clarke
The Nine Billion Names of God
(Star Science Fiction Stories, 1953)
-- Vol. #2
The Star
(Infinity Science Fiction Nov 1955)
-- Vol. #5
A. J. Deutsch
A Subway Named Mobius
(Astounding Dec 1950)
-- Vol. #4
Philip K. Dick
Impostor
(Astounding Jun 1953)
-- Vol. #2
Thomas M. Disch
Come to Venus Melancholy
(F&SF Nov 1965)
-- Vol. #7
Francis Donovan
The Short Life
(Astounding Oct 1955)
-- Vol. #4
Kelley Edwards
Counterspy
(Astounding Dec 1953)
-- Vol. #3
Tom Godwin
The Cold Equations
(Astounding Aug 1954)
-- Vol. #3
Robert A. Heinlein
Blowups Happen
(Astounding Sep 1940)
-- Vol. #2
Zenna Henderson
Food to All Flesh
(F&SF Dec 1953)
-- Vol. #3
Henry I. Hirshfield
On Handling the Data
(by HIH & G. M. Mateyko)
(Astounding Sep 1959)
-- Vol. #5
Roy Hutchins
The Nostalgia Gene
(Galaxy Nov 1954)
-- Vol. #6
Raymond F. Jones
Noise Level
(Astounding Dec 1952)
-- Vol. #5
Gerald Kersh
The Copper Dahlia
(Argosy (UK) Oct 1949)
-- Vol. #2
Daniel Keyes
Flowers for Algernon
(F&SF Apr 1959)
-- Vol. #4
Damon Knight
Four in One
(Galaxy Feb 1953)
-- Vol. #3
C. M. Kornbluth
The Altar at Midnight
(Galaxy Nov 1952)
-- Vol. #2
Henry Kuttner
Camouflage
(Astounding Sep 1945)
-- Vol. #6
Or Else
(by HK & C. L. Moore)
(Amazing Aug/Sep 1953)
-- Vol. #1
R. A. Lafferty
Snuffles
(Galaxy Dec 1960)
-- Vol. #7
Philip Latham
The Xi Effect
(Astounding Jan 1950)
-- Vol. #1
Fritz Leiber
Later Than You Think
(Galaxy Oct 1950)
-- Vol. #5
Murray Leinster
The Wabbler
(Astounding Oct 1942)
-- Vol. #3
Katherine MacLean
Pictures Don't Lie
(Galaxy Aug 1951)
-- Vol. #1
G. M. Mateyko
On Handling the Data
(by Henry I. Hirshfield & GMM)
(Astounding Sep 1959)
-- Vol. #5
J. T. McIntosh
The Bliss of Solitude
(Galaxy Jan 1952)
-- Vol. #4
First Lady
(Galaxy Jun 1953)
-- Vol. #1
Lion Miller
The Available Data on the Worp Reaction
(F&SF Sep 1953)
-- Vol. #3
C. L. Moore
No Woman Born
(Astounding Dec 1944)
-- Vol. #1
Or Else
(by Henry Kuttner & CLM)
(Amazing Aug/Sep 1953)
-- Vol. #1
H. Nearing, Jr.
The Cerebrative Psittacoid
(F&SF Aug 1953)
-- Vol. #1
Alan E. Nourse
The Coffin Cure
(Galaxy Apr 1957)
-- Vol. #7
Edgar Pangborn
Angel's Egg
(Galaxy Jun 1951)
-- Vol. #2
The Music Master of Babylon
(Galaxy Nov 1954)
-- Vol. #7
Rog Phillips
The Yellow Pill
(Astounding Oct 1958)
-- Vol. #4
H. Beam Piper
He Walked Around the Horses
(Astounding Apr 1948)
-- Vol. #3
Frederik Pohl
The Children of Night
(Galaxy Oct 1964)
-- Vol. #7
A Life and a Half
(If Jul 1959)
-- Vol. #6
Arthur Porges
The Fly
(F&SF Sep 1952)
-- Vol. #6
The Ruum
(F&SF Oct 1953)
-- Vol. #1
Kit Reed
Judas Bomb
(F&SF Apr 1961)
-- Vol. #6
Maurice Richardson
Way Out in the Continuum
(Horizon Mar 1946)
-- Vol. #7
Eric Frank Russell
Hobbyist
(Astounding Sep 1947)
-- Vol. #4
A Present from Joe
(Astounding Feb 1949)
-- Vol. #1
Ultima Thule
(Astounding Oct 1951)
-- Vol. #7
The Waitabits
(Astounding Jul 1955)
-- Vol. #6
Michael Shaara
Grenville's Planet
(F&SF Oct 1952)
-- Vol. #3
Robert Sheckley
The Monsters
(F&SF Mar 1953)
-- Vol. #5
Clifford D. Simak
Green Thumb
(Galaxy Jul 1954)
-- Vol. #5
Worrywart
(Galaxy Sep 1953)
-- Vol. #2
Cordwainer Smith
The Game of Rat and Dragon
(Galaxy Oct 1955)
-- Vol. #3
Evelyn E. Smith
BAXBR/DAXBR
(Time to Come, 1954)
-- Vol. #4
Margaret St. Clair
Prott
(Galaxy Jan 1953)
-- Vol. #1
Theodore Sturgeon
When You're Smiling
(Galaxy Jan 1955)
-- Vol. #2
A. E. van Vogt
Dormant
(Startling Stories Nov 1948)
-- Vol. #1
Jack Vance
The Gift of Gab
(Astounding Sep 1955)
-- Vol. #3
Kurt Vonnegut, Jr.
Harrison Bergeron
(F&SF Oct 1961)
-- Vol. #7
John Wyndham
Consider Her Ways
(Sometime, Never, 1956)
-- Vol. #5
Dumb Martian
(Galaxy Jul 1952)
-- Vol. #1
Una
(F&SF Jan 1953)
-- Vol. #2
Roger Zelazny
The Doors of His Face, the Lamps of His Mouth
(F&SF Mar 1965)
-- Vol. #7