Hi, I'd like to help you with your question.
This may be an obvious first step, but have you asked him to leave you alone? Sometimes, people in relationships can get the wrong idea about a break up, especially men. They may interpret your breakup as you playing hard to get. Make it clear to him (only if you feel safe doing this) that you are done with the relationship and you want him to leave you alone, for good.
If you have done that and he still will not leave you alone, there are steps you can take to help the situation:
If you feel he is a danger, contact the police. Tell them he is stalking you. They may not be willing to do anything at this point if there is no evidence, but ask if you can file a report and/or file a restraining order. This will establish a paper record of his actions.
Gather all the support you can. Do you have brothers or male friends that can go with you when you think you might see your ex? Stay closer to your sisters and/or friends too. Do not go anywhere alone if you can help it. If you do, stay near crowds or in clear sight of other people.
Call the phone company and tell them about the harassment. Ask to have his number blocked. Make your number private and do not give it to anyone who is not essential in your life. Do not provide it anywhere on the internet. If you are asked to provide your number for something, give a work number or the number of a friend (with their permission).
If you feel you are in danger, buy mace or keep other self defense items with you. Keep emergency phone numbers handy and on speed dial. Keep your phone in your hand when you are out in public. Be aware of your surroundings.
Given time, most ex's lose interest. Unless he does something overt and illegal, you may have to wait him out.
I hope this helps you,