An amphitheatre is an open-air venue used for entertainment; performances; and sports.
ancient roman amphitheatres were oval or circular in plan; with seating tiers that surrounded the central performance area; like a modern open-air stadium. in contrast both ancient greek and ancient roman theatres were built in a semicircle; with tiered seating rising on one side of the performance area.
modern parlance uses "amphitheatre" for any structure with sloping seating; including theatre-style stages with spectator seating on only one side; theatres in the round; and stadia. they can be indoors out outdoors.