Sound mixer who mixes the show at the sound-board. Often they will work in the sound shop in pre-production to build the sound package - mics, speakers, amps, processors, cabling, etc. - everything that is required by the sound designer.
In the theater, they are in charge of installing the sound system - hanging speakers, running cable, and setting up microphones. Once actors are onstage they operate the show. This means mixing all mics and operating all playback - music tracks, sound effects. In a busy play or in a musical they will have a script with their mic cues in it, they will also take cues from the SM.
A2: Assistant to sound mixer
The A2 is on the deck and will assist in checking the sound system pre-show including battery-ing up all mics and checking them, then distributing them to cast. They monitor mics throughout the show and will troubleshoot problems as they arise.