Complaint Repairs take too long - what to do?

A good three weeks ago I gave a faulty notebook to MediaMarkt for repairs. This continues to this day.

If possible, I would like to set a deadline for the dealer to then initiate a withdrawal from the purchase if necessary.

Is that possible - and if so: how should I inform the dealer? So by post, email, etc.

You should have agreed with the dealer at the beginning of a reasonable period by when the repair should be finished. But yes, you can still set him a deadline, but it must be reasonable. Depending on the case, 1 week to 1 month is appropriate. Would email the dealer about this.