According to greek legend, what sets off the trojan war?

The goddess Eris gave a golden apple to the fairest of the three goddesses, Aphrodite, Athena and Hera. Zeus couldn't choose, so he asked Paris to judge. Every goddess payed a visit with a proposal if she won, Paris would get something. Paris found Aphrodite's proposal the most interesting: Getting the most beautiful woman. He picked Aphrodite, and she made Helen, fiance of the brother of Agamemnon, king of Mycanea, fall in love with Paris. Paris took Helen to Troy, without permission of course. As revenge, Agamemnon sent troops to siege the city and take it.