While it is asumtion than an Italian by the name of Gaetano Vinaccia was the first person in guitar history to create the frame of an acoustic guitar. But a guy from Spain whose name was Antonio Torres Jurado is given credit for building the first guitar that we recognize today.
The most important piece of the body is the soundboard. It is the wooden piece in front of the guitars body, and it's job is to make the guitar's sound loud enough to hear.