Greek Theatre
Greek theatre began as a religious ceremony called City Dionysia, which honored on the Greek god Dionysus. This festival was performed in Athens every March. During this festival, men would perform songs to welcome Dionysus. Plays were only presented during the time of this festival. In the earlier festivals actors, directors, and dramatist were the same person. Later on, three actors were allowed in each play. The actors were generally amateur and not professionals, and they were always all male. Business and activities were suspended during the week-long festival. It was considered a civic duty for people to participate in the productions in some way. The plays were performed to give a lesson to the people. The forms of theatre were drama, comedy, and satyr. The comedy and tragedy plays that began in Athens have influenced nearly all Western drama.
Satyr: Satyr plays are among the earliest known plays.
Greek custom during the City Dionysia was developed so that competing playwright presented a trilogy of tragedies rounded off with a light-hearted satyr play. A satyr would usually use a common myth, make fun of it, and almost disrupt the set course for the myth, but in the end the traditional resolution of the myth would be conserved. Satyr plays gave way to comedy as the principle form of humorous drama and were no longer written.
Tragedy: The first known Greek actor and the originator of the tragedy genre is considered to be Thespis. The word tragedy actually translates into “goat song,” which may refer to the goats that were sacrificed to Dionysus before each performance. Three well-known Greek tragedy playwrights are Sophocles, Euripides, and Aeschylus.
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Comedy mask

Comedy: Greek comedy is split into three periods: Old Comedy Middle Comedy, and New Comedy. There are eleven surviving plays written by Aristophanes from the Old Comedy period, which still exist today. This type of play contained choral dances, masked actors, poetic meters, scenery and stage mechanisms, and the dramatic form of Attic Greek.Old Comedy influence can be seen today in Saturday Night Live and Monty Python. Comedy plays arose from imitation, such as when partiers sang songs in which they teased, mocked and made fun of spectators or public figures.
Structure of a Theatre:
During a performance there were no props or sets used. The actors’ lines marked the passage of time and the setting. The design of the theater was very important for acoustics because there were no microphones.
Orchestra:
The orchestra was a large circular area at the center of the theatre where the performance was presented.
Skene: The skene was a large building behind the orchestra, which was used as a backstage for the actors to change their costumes and masks. The structures were sometimes painted to provide a backdrop.
Parados: The parados were two broad aisles which allowed the chorus to enter the theater.
Theatron: The theatron held benches on which the audience sat. It was specifically built into a hillside to provide good views of the action.
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Theatre at Epidaurus
Actors: Participation in the plays was a civic duty and many would volunteer for the chorus. Experienced speakers were the ones that became actors, so they were often government officials or important businessmen. Actors were admired and
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Ancient Greek Actor
exempt from military duty. Women were not allowed to become actors and had to sit in the higher seats of the theatron. The large size of the theatre and the distance of even the nearest spectators from the performers made a non-naturalistic approach to acting necessary. Every gesture had to be large and definite so as to be seen from the back rows. Facial expression would have been invisible to everyone, except for the closest members of the audience. The actors could not move easily, so lines were delivered in a “speech” style. They also used broad sweeping gestures and general movements to express emotions, such as bowed head to show grief, beating their chest to show mourning, or stretching arms to show prayer.

Masks: The masks were made from wood, leather, or cloth and flour paste. Comedy masks were often depicted with smiling or leering expressions and tragedy masks were often depicted with mournful or pained expressions.

Some versions of Greek plays are still put on today. Medea is one of them. The original play was written by Euripides, and of course there would not have been a woman acting in the original play.

Sources:
http://www.ancientgreece.com/s/Theatre/
http://ancienthistory.about.com/od/greekliterature/a/aa081099tragedy.htm
http://www.usu.edu/markdamen/ClasDram/chapters/081earlygkcom.htm
http://www.newworldencyclopedia.org/entry/Ancient_Greek_Comedy#Influence