I would recommend you watch it in a theater (if it's still showing where you live), if only for the spectacular soundtrack.

I enjoyed the movie even more than the original short story "Story Of Your Life". Which is very rare. "Arrival" is not perfect, but very good.

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/

Thanks for the link. Mentioned elsewhere that Wolfram's software was used live in filming to analyze the semagraphs. But, I missed the Wolfram blog post. Am going to see the movie again particularly for that sequence (plus the Jóhann Jóhannsson soundtrack floors me).

There was a HN discussion of that blog post, as well: https://news.ycombinator.com/item?id=12940364

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.

It's an interesting "interpretation" of the short story, but it trades a lot of the beautiful ideas for a more generic alien contact story, though the core plot remains the same.

I said it in another comment, but I seemed to enjoy the movie less because I had read the short story.