Quantitative parts:

Prologue: The part preceding the entry of the chorus. When not omitted, it is either a monologue or a duologue. The prologue was instituted by Sophocles.
Parodos: The song of the chorus while entering.
Episode: The parts, consisting of dialogue, that take place between actors or between actors and chorus. The episodes are the dramatic part of the play par excellence, containing conflict between characters and moving the action forward.
Stasimon: A song or ode sung by the chorus at the end of any episode. Once having entered the orchestra, the chorus (consisting of two semi-choruses) never leaves it. It is 'static' there - hence the name stasimon. A stasimon has a set or sets of strophe, antistrophe, epode. The music accompanying song and dance was from a pipe played by the piper from behind the stage altar.
Exodus: The final part of the play, closing with the exit song of the chorus. The rhythm of this song 'supported' the chorus' exit.
Kommos: Dirge sung by the chorus and an actor (or two actors) alternately. The parodos could take the form of a kommos.
Monody (dyody): Song sung by one actor (by two actors together).

Qualitative parts:

Ploke (Web): The way the playwright interwove incidents and linked them together.
Peripeteia (Reversal of fortune): The change of the hero - from unhappiness to happiness or vice versa.
Anagnorisis (Recognition): The way two (or more than two) characters in the play recognize one another, having previously been unaware of each other's existence or true identity.

The myth: The story which the playwright turns into a play - the plot, in other words. The subjects of myths in drama were drawn by the playwrights from mythology, very rarely from history.
Lexis (Diction): The way the playwright handles language and text.
Melos (Tunes): The musical elements of the play.
Opsis (Visuals): Stage sets and costumes.
Props: Mask, costume appropriate to the gender, age, rank and character of the principal character, symbols of authority.
Originally masks were of clay; later they were of leather. They portrayed the constant character of the hero schematically. Costume and buskins (shoes with platform soles) were worn by actors to give the human body superhuman stature. All these elements, whether they went beyond the scenic means or were used in parallel with them, helped alienate the spectator from the actor.
Ethos (Temper): The character of a hero of drama; the way he/she reacted to circumstances.
Dianoia (Intent): The way the playwright expressed his own thoughts, ideas and views on the world and life in general through his heroes; and also the techniques he used to support these views of his.