Those most commonly cited are:
• "There shall be no compulsion in religion" (Surah 2:256, all quotes from the Dawood translation, 1999). This is often quoted to say Islam doesn't compel conversions to Islam or prevent people from leaving Islam for another religion.
• "Whoever killed a human being, except as punishment for murder or other villainy in the land, shall be regarded as having killed all mankind; and that whoever saved a human life shall be regarded as having saved all mankind" (Surah 5:32). This is often cited to show that Islam condemns violence and holds human life in high regard.
• "Say, 'Unbelievers [non-Muslims], I do not worship what you worship, nor do you worship what I worship. I shall never worship what you worship, nor will you ever worship what I worship. You have your own religion, and I have mine" (Surah 109:1-6). This is often quoted to say that Islam takes an accepting view toward others being able to practice their own religions.
• "If they incline to peace, make peace with them, and put your trust in [Allah]. It is surely He who hears all and knows all" (Surah 8:61). This is often cited to say that Islam teaches living at peace with others.
Some even say that the word Islam means "peace," though this isn't true. Islam means "submission"—submission to Allah, Islam's deity. The meaning of Muslim, a person who practices the religion of Islam, is "one who submits"—who submits to Allah and his religion.
While the verses quoted here seem fairly clear, what the Quran actually teaches isn't so straightforward. Dozens of verses, a few of which are quoted in the main article "The Jihadist Worldview," clearly advocate warfare, violence and brutality. So why the clear contradictions?
Much of the confusion stems from the circumstances under which the Quran was written. Muhammad, the founder of Islam, was illiterate, so he didn't write a word of the Quran. The 114 chapters of the Quran, called surahs, record the supposed revelations of Muhammad as written down or memorized by his followers after Muhammad came out of trance-like states during which Allah supposedly disclosed his divine thoughts.
In the years following Muhammad's death in A.D. 632, his closest companions compiled these writings into the Quran, which Muslims consider to be the divine and authoritative words of Allah.
However, unlike the Bible, the Quran isn't organized historically, chronologically or thematically. It's organized based on the length of the chapters, from longest to shortest, regardless of content or timing. Thus, when verses conflict, no one can really tell for sure which verses were written earlier and which were written later (and thus presumably the "final word" on a given subject).
Such inherent contradictions led to the Muslim doctrine of abrogation, meaning earlier verses were abrogated—nullified or overridden—by later verses. This doctrine is based on two verses that Muslims believe Allah inspired to be included in the Quran:
• "If We abrogate a verse or cause it to be forgotten, We will replace it by a better one or one similar. Did you not know that [Allah] has power over all things?" (Surah 2:106).
• "When We change one verse for another ([Allah] knows best what He reveals), they say: 'You [Muhammad] are an imposter.' Indeed most of them have no knowledge" (Surah 16:101).
Islamic scholars and teachers are well aware of this teaching, though they seldom discuss it openly because of its inescapable implications—that Allah, far from being an all-wise and all-knowing deity, can and did change his mind in what was supposedly divinely revealed to Muhammad.
What are the practical conclusions that result from the doctrine of abrogation?
Most scholars who have studied the Quran believe that the Quran's verses advocating peaceful coexistence and tolerance were written in the early years of Muhammad's movement when he and his small number of followers didn't wish to antagonize potential enemies who greatly outnumbered them. But as Muhammad gained more and more power and a greater following, the chapters of the Quran written later increasingly advocated warfare, violence, intimidation and enslavement of those who opposed him.
Thus, Allah's later revelations command fighting and subjugation of "infidels"—non-Muslims—so that Islam would gain its rightful place as the dominant (or only) religion in lands it controlled.
Which is exactly what we see playing out in headlines all around the world.