The story of Troilus and Cressida is mediaeval in origin, and is not part of Greek mythology. Shakespeare drew on a number of sources for his play, in particular Chaucer's version (Troilus and Criseyde). Chaucer's source was Boccaccio's Il Filostrato, which in turn derives from a 12th–century French text: Benoît de Sainte–Maure's Roman de Troie. Shakespeare also drew on Homer's Iliad for some plotlines, and on various medieval and Renaissance retellings.
The story was a popular one for dramatists in Shakespeare's day, and he may have been inspired by contemporary plays.
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