Oh Columbia Library, how I love thee.
My dad recommended this to me (with the caveat that he hadn't actually read it in decades) and when I found it I had to give it a look.
I had actually just finished reading Sholem Aleichem's Tevye stories out-loud to my girlfriend, and it made lots of sense to start the same way with the first story in this collection: On Saturn, Have We Got a Rabbi. It's essentially a sci-fi Tevye story that is pitch-perfect (with Aleichem's originals, not exactly with the musical), and it gives one of the best descriptions I have ever seen of the general cycle of anti-Jewish prejudice (something that has been described many times) while being very funny--just like a Sholem Aleichem story.
Also, you can hear the story's author, William Tenn, read it right here:
On the whole (though I haven't read everything here) it's quite good, although a lot of the same ground is covered by different stories (surprise!). Most interestingly, many are set in futures in which it is very clear that the treatment of Jews is a cycle, and that this post-Holocaust era was just a quick blip of us being alright before everyone started shitting on us again.