A very good intro is also http://blog.stephenwolfram.com/2016/11/quick-how-might-the-a...
by Stephen Wolfram who helped with some science parts on the movie.
My short review: https://letterboxd.com/rurban/film/arrival-2016/1/
Also I'll chime in about the soundtrack; I loved it. Lucky me Google Play Music has it - it says I've listened to it about 9-10 times through so far.
I said it in another comment, but I seemed to enjoy the movie less because I had read the short story.