The tone of this play is established in the Prologue:
Sixty and nine, that wore
Their crownets regal, from th' Athenian bay
Put forth toward Phrygia, and their vow is made
To ransack Troy, within whose strong immures
The ravish'd Helen, Menelaus' queen,
With wanton Paris sleeps -- and that's the quarrel.
The flippancy of those last four words suggests the folly of the enterprise to unfold before us. Shakespeare takes the most famous military adventure in history, the siege of Troy, and turns it upside down. Here are no extraordinary heroes fighting boldly in a struggle complicated by the actions of the gods. Here instead are petty and vicious plotters caught up in an endless war that never made much sense, and now, after seven years of slaughter, makes even less. That Troilus and Cressida apparently was not performed before 1898, yet has been staged regularly since, is appropriate. For this play, perhaps more than any of Shakespeare's, speaks especially to our century, when so many works of art have dramatized the madness of war.
The story of Troilus and Cressida was a popular medieval tale, and Shakespeare was probably acquainted with Chaucer's romantic retelling, Troilus and Criseyde. But medieval writers also exalted courtly love and scorned what they judged to be the crude customs and mores of the Greeks. Cressida herself is mocked in several medieval works, and Shakespeare probably knew one of the most famous, Robert Henryson Testament of Cressid, composed in the latter part of the fifteenth century.
Many of the events of this play are taken from the Iliad of Homer, and Shakespeare was likely influenced by Chapman's translation. Dominating the Iliad, however, is a sense of tragedy, as human beings of stature, always conscious of their mortality, battle fiercely in a drive for national and personal glory.