The airco compressor of your Audi pressurises the air conditioning gaz before it is injected into the aircon system. Audi compressors tend to be rather big and heavy car parts. They are equipped with a pulley so that the compressor can be attached to the drive belt. The drive belt drives the compressor. So if your compressor doesn't seem to be working, this could easily be a drive belt rather than a compressor problem. To avoid a failing ac due to a snapped drive belt, remember to check your drive belt regularly, at least once a year.
If your air con is not blowing cool air, it doesn't necessarily mean your compressor is completely broken. Usually it just means it's run out of gas. In that case, drop by your local garage to have it filled. If however the car part itself is completely failing and need replacing, you'll find a large variety of air con compressors here. To ensure it fits to your car, please specify your Audi's model and engine in the drop-down menu.