When discussing Greek drama, the subject of Aristotle's Poetics frequently turns up, since not only is it a fascinating piece of criticism, but it also gives us a lot of evidence about the origins and history of classical tragedy.
Aeschylus with first increasing the number of actors from one to two, and Sophocles with adding a third actor. Sophocles, according to Aristotle, also introduced painted scenery to tragedy.
The sixth chapter of The Poetics is the most famous. In it, Aristotle lays out his theory of catharsis, a purgation through pity and fear. He also catalogues the component parts of tragedy: plot, character, language, thought, spectacle, and melody. Of these, The Poetics singles out plot as the most important, since tragedy is not an imitation of people, but of their actions.
Plot, according to Aristotle, must be complete, with a beginning, a middle, and an end. In order to be beautiful, it must also have a size or magnitude appropriate to it. Plays must not be so long that we cannot hold them in our memory, and Aristotle writes that at one time tragedies were timed by water clocks, or at least some people people say so. (I wonder what would have happened if a play went over the time limit!)
Aristotle is opposed to episodic drama, in which actions follow one another in no probable or inevitable sequence. Instead, he recommends the use of reversals and recognition scenes, which work best when they go together to cause suffering, or pathos.
Later on, Aristotle's vague suggestions got taken for hard-and-fast rules all playwrights had to follow. If we take his advice as it was meant, helpful hints rather than dictates, The Poetics can be a useful resource for dramatists even today.