According to Wikipedia: The name amphitheater (alternatively amphitheatre) refers to a level, open space surrounded by an oval area that gradually ascends. The area may be a man-made structure or a natural geographic formation, but it is suited for seating people on the sloping area for the viewing of spectator sports, games, concerts, displays, rallies, or theatrical performances. An amphitheater can be classified as either an Ancient Amphitheater, a Contemporary Amphitheater, or a Natural Amphitheater.
Three Classifications of Amphitheaters:
Ancient Amphitheaters: An ancient amphitheater is particularly associated with ancient Rome and ancient Greece and was used for various types of public spectacles. In the Roman Empire, amphitheaters were round or oval in shape, forming a complete circle or ellipse, and were used for spectator sports, games, and displays. This is in contrast to a Greek classical amphitheater, which was semi-circular and used for theatrical performances (also gladiators). Click Here for Links to Some Examples of Ancient Amphitheaters.
Contemporary Amphitheaters: A contemporary amphitheater is a curved, acoustically vibrant performance space, particularly one located outdoors. Contemporary amphitheaters may include standing structures, sometimes curved or "bowl" shaped (referred to as bandshells), both behind the stage and behind the audience, creating an area which echoes or amplifies sound, making the amphitheater ideal for musical or theatrical performances. Click Here for Links to Some Examples of Contemporary Amphitheaters.
Natural Amphitheaters: A natural amphitheater is a performance space located in a spot where a steep mountain or a particular rock formation naturally amplifies or echoes sound, making it ideal for musical and theatrical performances. Notable natural amphitheaters include the Drakensberg amphitheatre in Drakensberg, South Africa, and the Echo amphitheatre, Cedar Breaks National Monument, and Red Rocks Amphitheatre, all of which are in the United States. Click Here for Links to Some Examples of Natural Amphitheaters.