Self-Addressed Stamped Envelope
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SASE (SAE in the UK) is an envelope with your address on the front and a postage stamp in the corner. It stands for "Self-Addressed Stamped Envelope." It was a common way to distribute materials for both fannish and professional purposes prior to the turn of the 21st century.
In many ways, a SASE was the automated 'reply' button of the pre-internet age.
Spelling and Pronunciation
: Pronounced: "Sassy." 
: "Which is correct, "a" SASE or "an" SASE? I use "a" because I pronounce SASE as as one syllable word. Others prefer "an" because they are more comfortable spelling out the word as four separate letters. No matter how you pronounce it, be sure to include it! Most fan-related activities are very not-for-profit." 
Sometimes editors simply requested they be sent just the postage stamps. This was intended to reduce the effort and cost with replies.
From a zine's editorial
A fan sums it up in Communications Console: "And forget not thy SASES..."
SASEs: A Constant Source of Scolding and Explanation
Despite the fact that SASEs were an expected standard in fandom, fans needed to be constantly reminded to use them.
A zine editor scolds fans who do not enclose an SASE with their inquiries:
This is a violation of one of the most important and honored laws of fandom. SASE ANYBODY you want a reply from. Relatives and folk you correspond with on a firmly regular basis are exempt, but not by much. 
SASEs: A Paper Nightmare
I have limited filing space in my office and I have three files for SASEs: Chalk and Cheese/Hols/Brit Shriek!; Green Eggs and Ham; and Blake, Rabble and Roll. When people send me a SASE asking to be notified when a particular zine comes out, I put it in that file. When the zine comes out, I pop a flier in the envelope and send it out. No problem. But when people send me five, six, seven SASEs and ask to be notified 'of whatever comes out next, but no QL zines, or 'no Professionals zines, just Blake's 7 zines,' I go crazy. I have a hard enough time keeping track of everything as it is. Please, people! Label your SASEs as to what zine you want a flier for, and DON'T ask for one that's available now and one that won't be printed for another six months in the same envelope. You won't get either until the second zine is out. 
However, not all cases actually involved stamps; some involved money orders for the cost of postage, and in many cases the materials were too bulky for envelopes, so those were also not included. Envelopes were often replaced with self-addressed self-stick labels to be placed on packaging provided by the distributor. Nonetheless, the term remained in use.
- The All-Powerful SASE by Charlotte Frost, posted February 2013; WebCite
- SASE defined by Susan Garrett