Is it normal for me to still be with him

i have been dating this guy, he is 11 years older than me(am 19). He has been cheating on me, the first time i caught him i forgave him. And now am suspecting that he is cheating again, (but i have no prouf) but now with two girls. I know that because i read his sms, not to forget, before i met him he was dating this girl and they broke up because the girl was married and the husband found out and he tried to hurt him. When we started dating he told me he had a fiance but she is out of the country, months later he told me that it was over, not knowing he was lying. One day i accidentally opened his mail box( he did not sign out) and i saw a letter he sent to her, telling her how much he loves her, and how he was planning his future with her. When am with him i feel fine, and he does not treat me bad, but when i think about all these things, i asked myself what am i still doing with him. SOULD I BREAK UP WITH HIM?.