A comic book series published by Marvel Comics in the early 1960s. The title Amazing Adult Fantasy has a pornographic sound to modern sensibilities, but in the more innocent era in which it was published (well after the 1950s hysteria against comics as a corrupter of youth resulted in the imposition of the squeaky-clean Comics Code Authority, and a few years before underground comix brought sex, drugs, and rock & roll into the comics world) the title merely indicated the publisher's desire to seek a slightly more mature audience from the traditional comic reader of the time. The cover blurb billed it as "The Magazine that Respects Your Intelligence". It apparently didn't succeed in catching this adult comic-reader audience, as it got cancelled after just over one year.
The series began as Amazing Adventures (June 1961) and took on the Amazing Adult Fantasy name with issue #7 (December 1961). With issue #15 (August 1962) it changed its name again, dropping the "Adult" to be just Amazing Fantasy, but that proved to be its last issue (at least until 1995, when Amazing Fantasy #16 through #18 were released).
The early Amazing Adventures issues featured stories written by Stan Lee and drawn by Jack Kirby and Steve Ditko, largely the sort of monster stories that Atlas / Marvel was known for in that pre-superhero era. However, Dr. Droom (not to be confused with Dr. Doom) appeared several times and is sometimes regarded as "Marvel's first Silver Age superhero". (He later resurfaced as Dr. Druid.)
With the title change to Amazing Adult Fantasy, the stories attempted to have more thoughtful, idea-centered content instead of just scary monsters (though, like just about all comic-book SF / fantasy / horror in the Code-approved era, it was a pale imitation of the great EC works of a decade earlier). Kirby was taken off the title and Ditko did the artwork for the rest of its run (except for the cover for #15).
With the title facing cancellation, the publisher decided to use its last issue as a "trial balloon" to test out a new character, created by Lee and Ditko, that was too uncertain to risk giving his own book yet -- this was Spider-Man. Sales of that issue proved to be very strong, prompting the launch of Amazing Spider-Man as a separate series in 1963. Jack Kirby did the cover of issue #15 after an earlier version drawn by Ditko was rejected.
The three issues released in 1995 featured stories of Spider-Man taking place between AF#15 and the debut of his own title, Amazing Spider-Man #1.
Amazing Adult Fantasy was also the title of an album released by the band "Barnes & Barnes", the members of which (including Lost In Space actor Bill Mumy) are comic book fans. The album cover featured the cover of one of the issues of the comic book of that name.