I have no doubt that there are "many lies" concerning Islam on the Internet, so allow me to go over what's true. While most Muslims are exceptionally gracious and peace-loving people, anyone who wants to commit violence has perfect justification for doing so from the Koran.
While violence in the Koran is sometimes for self-defense, at other times it is open-ended. Many passages in the Koran exhort Muslims to hate or kill or terrorize infidels (non-Muslims) wherever they find them.
See Suras 2:190-193, 2:216, 2:244, 3:56, 3:151, 4:56, 4:74, 4:76, 4:89, 4:91, 4:95, 4:104, 5:51, 5:32-38, 7:96-99, 8:12-14, 8:39, 8:60, 8:65, 9:5, 9:14, 9:23-30, 9:38-41, 9:111, 9:123, 22:18-22, 25:52, 47:4, 47:35, 48:16, 48:29, 61:4, and 66:8-10. (Note: English translators of the Koran sometimes try to soften the true Arabic meaning of some of these passages. For example, to "fight" really means to kill in Arabic.)