By the way, this is a slightly nuanced question. Usually we address the question "Is Islam a Religion of Peace?" and this allows people to provide peaceful passages, ignore all the violent ones, and answer the question by saying "Of course!" Well, now we're asking "Is Violence Taught in Islam?" No getting around it this time.
Fight those who believe not in God nor the Last Day, nor hold that forbidden which hath been forbidden by God and His Apostle, nor acknowledge the religion of Truth, (even if they are) of the People of the Book, until they pay the Jizya with willing submission, and feel themselves subdued.
But when the forbidden months are past, then fight and slay the Pagans wherever ye find them, an seize them, beleaguer them, and lie in wait for them in every stratagem (of war); but if they repent, and establish regular prayers and practise regular charity, then open the way for them: for God is Oft-forgiving, Most Merciful.
Allah's Apostle said: "I have been ordered (by Allah) to fight against the people until they testify that none has the right to be worshipped but Allah and that Muhammad is Allah's Apostle..."
Allah's Apostle said, "I have been ordered to fight the people till they say: 'None has the right to be worshipped but Allah.'
While we were in the Mosque, the Prophet came out and said, "Let us go to the Jews" We went out till we reached Bait-ul-Midras. He said to them, "If you embrace Islam, you will be safe. You should know that the earth belongs to Allah and His Apostle, and I want to expel you from this land...
"...Allah's Apostle said, I have been ordered to fight the people till they say 'None has the right to be worshipped but Allah'... "
It has been narrated on the authority of Abdullah b. 'Umar that the Messenger of Allah said: I have been commanded to fight against people till they testify that there is no god but Allah, that Muhammad is the messenger of Allah...
Invite them to (accept) Islam; if they respond to you, accept it from them and desist from fighting against them... If they refuse to accept Islam, demand from them the Jizya. If they agree to pay, accept it from them and hold off your hands. If they refuse to pay the tax, seek Allah's help and fight them...
It has been narrated by 'Umar b. al-Khattib that he heard the Messenger of Allah (may peace be upon him) say: I will expel the Jews and Christians from the Arabian Peninsula and will not leave any but Muslim.