Theater was born in Venice: this is a fact.
The first sort of theater arrangement known was in 1542, inside the noble mansion of the Gonellas in Venice. It was probably one of those situation in which a noble and absurdly rich family would be organize something (it was happening for concerts already) to entertain the youngs and their friends.
An evolution was the first real theater-only structure (made in wood) which was made in 1565, inside the city's convent, and it went on flames.
At this point the first real stone-made structure we know for a theater was the San Cassiano Theater, inside the Monastero della Carità, close to the Rialto Bridge.
It had an elliptical shape and two layers of boxes, unfortunately no images are left, because it was destroyed by a fire in 1629.
So, the San Cassiano Theater was rebuilt just in time for Carnival in 1637, with the idea of being open to the general public who paid a ticked to assist Operas and Melodramas, which was basically the idea of the shows to be held.
And this was truly the first theater in the world, basically dedicated to Opera, supposedly having the best acoustic available.
By the end of XVII century there were already 14 recognized theaters in Venice, as the idea caught up and was rewarded by constant flow of public.