Vertigo probably has the most complex plot of all Hitchcock movies. The story revolves around one central character, San Francisco police detective Scottie Fergusson. When he witnesses his partner fall to his death from a rooftop, he develops vertigo, or fear of heights.
Not long after he quits his job as a cop, an old friend of his from college (Gavin Elster) hires him to follow his wife who he thinks is possessed. But as Scottie investigates the life of this strange woman, he soon falls in love with her, and to reveal any more of the story would be a crime of the highest degree. Hitch would probably have me killed if I gave away the whole synopsis! So go see Vertigo if you haven't already.