Why does my Audi 80's engine rev high when I shift gears?

I notice that when I shift gears in my Audi 80, the engine rpm goes up significantly before settling back down. It's not causing any issues, but it's making me curious about why it's happening.

This can be a normal behavior for Audi 80s, especially in manual transmission models. It's called a rev hang and is caused by the engine computer keeping the throttle open for a short time after you let go of the gas pedal.