Theorem uses an ancient story form of a visiting stranger interfering in the lives of those with whom he or she interacts, changing them forever -- In the first half of the film. "the visitor" mysteriously arrives at the household of a comfortable bourgeois Italian family -- he is then, in a series of surreal scenes, seduced by the maid, son, daughter, mother and father -- As mysteriously as he arrived, he leaves -- In the second half of the film, we see the transformed lives of each family member -- In the end we are left with ambiguity -- What is the "theorem" that Pasolini is testing by this allegory? --
This is not a film of for a quick evening's romp, but deserves multiple viewing -- I suggest Jim Clark's commentary in the Links section for a more in depth discussion.