Story of Your Life by Ted Chiang many years ago. According to the helpful receipt I saved to use as a bookmark I bought the book on 2 Sept 2002 at around 9 PM. Details are fun! What was I doing at a (now defunct) Borders bookstore at 9 PM on a Monday? No idea. Buying books, obvs.
The story is a masterpiece, and it stuck with me over the years. The premise is deeply affecting, and the story itself is very well written. I loved it so much that when I heard they made a movie I dug the book off the bookshelf and re-read it again after over a decade.
You should read it if you like words, and books, and reading. The movie trailer outlines a much different narrative than the one described in the book. Also the story will probably take you less time to read. Even though the movie is getting great reviews they should be considered separately. The payoff of the story will be a lot better if you haven't seen the movie. So buy it, and read it. Think of the rest of the anthology as an excellent bonus.
As an aside: made a rare appearance at the local bar last night and a girl approached me and asked me if I was watching the football game on the tv. I said, no, not really. She said, 'oh because this time of year all the guys I know are obsessed with football'. I said, that's not me. She said, 'what do you do?' I said, 'I read books.' She would have been less surprised if I said "I kick puppies."