A cyberstalker can be a terrifying thing. If someone is harassing you or won't leave you alone online, then you need to take action. Don't fall into the trap of assuming that there is nothing you can do in such a situation. This is not the case. You can get proactive through your own Internet use and take action through legal channels if need be to make sure that you're protected from someone who has been stalking you online.
Contact your stalker, if you know who it is, and make it clear that you want all communication to cease. Be crystal clear, and after you have sent that message, never contact the stalker again, or respond to any communication you receive. (See Reference 1)
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Keep a record of every communication that your stalker sends you. Every e-mail, instant message, Facebook message or other communication should be saved from the point where you first feel threatened. That way, you have evidence to use should you need to take legal action.
Block the person from contacting you in as many ways as possible. This includes blocking e-mail addresses and removing the stalker from your social networking profiles, such as Facebook and Twitter. You may also want to change the privacy settings on your Facebook account so that only your friends can view your updates or photos. This prevents your stalker from gaining information about you that you wish to keep private.
Contact the police. Cyberstalking is a crime, and in certain cases, could lead to physical stalking and endangerment. Both federal and state laws are typically being broken if you are being cyberstalked. If you have evidence of the crime, and can confirm the identity of the stalker, especially if threats have been uttered, then you should have legal recourse.