IF Magazine was a monthly science fiction magazine that was first published in 1952, and ran through 1974, before it was merged into its sister publication, Galaxy Science Fiction. Now, you can read the entire run online over on Internet Archive.
IF never quite reached the same pinnacle as that of other magazines such as Astounding Science Fiction, the Magazine of Fantasy and Science Fiction or Galaxy Science Fiction, but it published a number of excellent stories and serializations, such as James Blish's classic story 'A Case of Conscience', and Harlan Ellison's 'I Have No Mouth and I Must Scream', and works from authors such as John Brunner, E.E. 'Doc' Smith, Joe Haldeman, Poul Anderson, James Blish, Frederik Pohl (who also edited the magazine), James E. Gunn, and many, many others.
Initially, IF sold poorly, but eventually made its way to Digest Publications and under the control of Frederik Pohl. While it initially didn't sell as well as its sister publication, Galaxy Science Fiction, Pohl used the magazine to publish entertaining stories, as well as serializations:
"Under Pohl If took on its own identity. Initially it had played second fiddle to Galaxy, but whereas Pohl kept the more select sf for that magazine, he turned If into a magazine for more adventurous and exciting sf: before long it was If that proved the more popular."
Pohl also used the magazine as a testing bed for newcomers, publishing numerous first sales from authors such as Larry Niven and Bruce McAllister.