Soundproofing???????????

The problem is that the wall is too solid. Vibrations on one side pass straight through to the other. You need to physically decouple your wall from theirs, which will not be cheap or easy. You could build another wall that is not attached to the present wall, but this makes no sense in an apartmet due to the excessive cost.

You need to either:

A. move, or
B. just crank it up so you can't hear them. Of course that will get you evicted, which brings us back to solution A.

1970,

I must agree with Herman. I even replaced the cheap insulation in my condo walls with 3M and it did not help that much. I have never really found any good advice on such a problem.

Brad Day
Atlanta, GA

Go to a hardware center, buy some cork tiles (thicker the better), use construction adhesive to attach them to the offending wall. Do all of the wall, don't leave any areas uncovered ('cept for electrical plugs and other fixtures of course). Worked for me in my office.