Unlike what the other reviewer stated, Michelangelo Antonioni's "The Story of a Love Affair" is not an adaptation of James M. Cain's classic "The Postman Always Rings Twice." That film is 1943's "Ossessione," also starring Massimo Girotti, and which was the first film by another great Italian director, Luchino Visconti. (And which is actually a better film, Girotti is certainly much better in "Ossessione.")
"The Story of a Love Affair" is structured as a noir/thriller. At the beginning, a jealous wealthy businessman in Milan hires a detective to find if his wife (Lucia Bose) is unfaithful and by doing so unwittingly rekindles her love for another man (Massimo Girotti), who may have been complicit with her on the death of her former best friend (who was also his fiancee). As their love affair progresses, the reunited lovers ponder killing the husband.
Although set up as a thriller, Antonioni is less interested in crime than in the psychology of the leading couple: an unhappily married society wife (Bose) and a down-on-his-luck former WWII soldier (Girotti). Lucia Bose, then only 19, is not a very good actress, but she's striking to look at, and Antonioni makes the most of her beautiful face. Girotti is not that great either, but he's also perfectly cast. The merits of this film really have to do with great visuals, not with great acting, so in that respect they're both excellent in their parts.
While not as great as other noirish debuts by great European directors, like Visconti's Ossessione or Malle's Elevator in the Gallows, "The Story of a Love Affair" is definitely worth checking out for fans of film noir or Antonioni.
The film looks pretty good on the DVD, but the extras disc was somewhat disappointing for me, though, especially the cheesily edited and rather cruel (namely the moment when an elderly Lucia Bose hugs a wheelchaired Antonioni) short about the release of the restored film. I would have preferred to see and hear more from Antonioni himself in the extras.