For live shows there's the Front Of House position, which is the person in the middle of the crowd mixing for the audience. Also a Monitor mixer who is on the side of the stage mixing what the band hears.
In broadcasting you have radio engineers, TV engineers, studio engineers, remote (on site) engineers and RF (wireless) engineers just off the top of my head. Movies productions also have several audio positions for before, during and after the actual filming.
I got a degree in audio engineering from Full Sail that has served me well for more than 20 years. Columbia College in Chicago also has an excellent program.