This is pretty straight forward folks. Violence is not an aberration in Islam—it is DOCTRINE. Dozens of passages in the Quran exhort Muslims to hate or kill or terrorize infidels (non-Muslims) wherever they find them. For examples, 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. These are the passages that jihadists quote in defense of their horrible atrocities.
While there are a couple of passages that Muslims point to that might suggest peaceful solutions (Suras 2:256, 29:46, 41:34), these are overwhelmed by the violent ones. Anyone who wants to commit acts of violence has perfect justification for doing so from the Quran.
You can look these passages up for yourself. Below is a site that has three translations of the Quran side-by-side. (Note: English translators of the Quran sometimes try to soften the true Arabic meaning of some of these passages. For example, to "fight" really means to kill in Arabic.)
http://www.usc.edu/org/cmje/religious-texts/quran
In addition to the Quran are the hadiths. These are collections of sayings and actions of Muhammad. These, too, are very violent.
For more information, see our Faith Facts article:
http://www.faithfacts.org/world-religions-and-theology/christianity-vs.-islam