Why does my Audi A4 engine stutter and shake at idle?

I've noticed that my Audi A4's engine shakes and stutters when the car is at idle. It seems to smooth out when I accelerate, but the shaking returns once I come to a stop. What could be causing this issue?

This could be caused by a malfunctioning idle control valve. This valve controls the air/fuel mixture when the car is idling and can become dirty or wear out over time. It's recommended to have it checked and replaced if necessary.