M.R.
Keep copies of them and contact your local internet service provider and possibly police if they are threatening. Print out hard copies to keep for your files.
Most people, unbeknownst to them although it is in there, sign contracts that they agree to use their internet service responsibly and legally. If they are sending you harassing/threatening messages or breaking the law, then they are in breech of their contract and can/should have their internet service discontinued.
Maybe try starting with police or your isp.