It was adapted from a novel called 'The Double'. Looks like the title was not available then changed it to 'Enemy'. Not a bad title either, but slightly misleads especially after watcher 'Prisoners'. Adam is a history professor and his life is a less joyous. His mother is worried about him for being careless. One day by chance he discovers something while watching a movie that knocks his inner consciousness. He begins to give more interest on it and prepare to solve the mystery. The venture he's after is supposed to take place smoothly, but it didn't. Hits back to his life and scatters the pieces of his own identity.

I must make you understand that it was like a jigsaw puzzle. The story just happens and it won't expose completely with proper description. Like the outer layer of a fruit, but inside there are lots of stuffs to figure it out by ourselves. If you are a smart enough, you will sketch your own conclusion by joining the pieces. For that you may need to watch twice. Revealing my opinion may end in spoiler, but wanted to say that the story was programmed to handle a man's irresponsibility and desire. Both were symbolically exposed its identity and rest of the things leaves for the audience to observe closely, otherwise you will miss the important point.
Never know how your day is gonna turn out. 
I yet to watch 'The Double', the description kind of match to this. Nowadays this thing keeps happening frequently like recently ones 'Olympus Has Fallen' and 'White House Down'. Anyway, Jake Gyllenhaal was awesome in this movie. Almost 90 per cent of the movie frames had captured his presence. Without a doubt its a one man show. He's becoming a great personality in Hollywood, but it was not a Hollywood flick. Finally, one more time I will remind you that it is not a piece of cake for everyone, choose it if you are not preferring entertainment.
8/10