Check your lease or rental agreement. A section of it ought to deal with noise and/or neighbor complaints. Then go see your landlord or manager about it. Worst case scenario, your city ought to have a noise ordinance. They can be cited for it, but that often unleashes bad feelings. Your landlord/manager is also an authority figure and will generally do a better job of smoothing things over.
And there is a physical solution to noise: soundboard. But if you don't own the place, it's probably not worth it. It'll probably be against the terms of your lease of rental agreement, too. In a nutshell, soundboard comes in sheets just like drywall and is usually placed behind the drywall. It cuts out a surprising amount of sound and isn't that expensive, either. Problem is, you've got to pull the walls off, apply it, and put up new drywall.
In addition to my day job, I work for my family, too. We have some apartments, and we *always* put up soundboard any time we renovate. Neighbor complaints drop almost to zero and it's an extra layer of insulation, too.