The giallo connection is confusing, so I'll just point out that the movie really isn't a giallo at all. It does give a lot of hints and bows, specially to the greatest works of Bava and Argento, but it's not preoccupied with these details at all, they remain details, and what the movie instead does is present a visual feast that you can only feel and experience. You're not doing yourself any favors by trying to follow a plot. I'd call Amer a drama, but that would also be misleading.
The movie is divided into three segments. In the first one we are in a spooky big mansion, following a little girl and her wandering about through rooms and hallways. She has a firm and hard looking mother dressed in mourning black. In one of the rooms lies a dead old man. She is consistently followed by a monstrous figure all dressed in black. Everything she experiences, she experience to the fullest and it's no use trying to part reality from dream world. When the little girl's feelings are strong enough, there seems to be no difference and the movie seems to continually express her mental world, rather than the "real". There is a magnificent, mindblowing scene where she catches her mother having sex with her lover. The incomprehensible sight causes the movie itself to literary break down. Words simply can't describe it.
In the second segment we see the same girl, now slightly older. But, certainly, not "old enough". We see her walk in sunlight, firmly side by side with her mother, both wearing summer dresses that dance along with the cinematography. Everywhere there are male predators. She runs away from her mother. She meet boys. She meet men. There is a tension and a danger in every shot, at times it seems as if the movie is breathing along with the characters, and it is impossible to tell if the danger is a thing of lust or a threat of death. In the third segment she is an adult, returning to the house of her childhood which now stands dead and abandoned. But the figure in black that haunted her as a child does not sleep.
I don't know when I will get the chance of seeing this movie again. It feels like a love story in my mind, I yearn and long for my long lost love. Will we ever see each other again? I can't deny that Amer is the definitive wet dream for a film critic or a film student, because it tempers with the limits of where narrative ends and imagery begins. It has the visual flair of Argento, but the perception of the characters and their world is as transcendent as in Tarkovsky's Mirror. The movie is jam packed with images that are surreal, deeply moving, sensual, scary and exceptionally beautiful. I keep feeling tempted to make silly metaphors like "the cinematography is making love with the editing" but you know what, that's exactly what this movie feels like. And I also think that it lays way beyond the shallow vanity that I guess you could accuse Argento for. I think the movie is expressing the feelings of the characters as they experience them. It is a rare thing in movies when you as a spectator can actually feel the heat of the sun, the sting from the thorn bushes, the spider crawling all over your body. It is unbelievably rare that we experience being given the look when the character feels it too. Most movies attempting to gain any kind of erotic charge fail for even trying. I have no idea how they manage to make it work in Amer. It is truly a fascinating piece of work that transcend from beyond the screen and somehow lures the audience in too. It might just be the most seductive film I have ever seen. From the insanely imaginative imagery in the beginning, to the profoundly striking close-range perspective in the adolescent middle, and the sheer weird and poetic amusement of the finale, Amer is just one of the rarest gems of movie making I have seen in a long time. I somehow have a feeling I won't be able to present my feelings for it in a proper way, and I do suspect it is a film that has to be seen to be believed, understood, experienced. I can, however, clearly state that it is one of the best movies I have seen this entire decade.