There is no the teaching of Islam. There is no central authority, no magestrum to give an official stamp on doctrine within Islam. A lot of people here are imposing their own religious bias (i.e that in Orthodoxy or Catholicism there is an official structure) on Islam.
There is at the very least a relative framework of official structure within Islam insofar as Muslims acknowledge the authority of (1) Koran, (2) important early Muslim commentators, (3) the Hadith, and (4) Sharia law, and well beyond that as Isa has pointed out, diversity notwithstanding.
Here someone may well say "all Muslims are not radicalized." That is surely true. But consider, if there are 1.57 billion Muslims worldwide, and -more optimistic than is surely reasonable- suppose 1% radicalized: we have 15.7 million radical Islamists. If closer to 10%, we have 157 million radical Islamists. It is not reasonable not to take this problem seriously. One should always keep what kind of critical mass has resulted in major problems historically and in our own century in mind.
The practical issue we face deals not with "True Islam" (True with a capital "T" -perhaps such a thing does not even exist, so what?) but Islam as we are with some statistically meaningful probability likely to find it in the world. So whether "Islam teaches" that Muslims should behead the Christians in my village is, I think, a distinction without much of a difference if Muslims who think so are beheading Christians in my village.
We might distinguish three Islams: Islam 1, Islam 2, and Islam 3. Islam 1 is what the Prophet taught, that is, his teachings as contained in the Koran. Islam 2 is the religion as expounded, interpreted, and developed by the theologians through the traditions (Hadith); it includes the sharia and Islamic law. Islam 3 is what Muslims actually did do and achieved, that is to say, Islamic civilization. If any general thesis emerges in this book it is that Islam 3, Islamic civilization, often reached magnificent heights despite Islam 1 and Islam 2, and not because of them...
...The treatment of women, non-Muslims, unbelievers, heretics, and slaves (male and female) was appalling both in theory and practice. In other words, Islam 1, Islam 2, and Islam 3 all stand condemned. The horrendous behavior toward women, non-Muslims, heretics, and slaves manifested in Islamic civilization was a direct consequence of the principles laid down in the Koran and developed by the Islamic jurists. Islamic law is a totalitarian theoretical construct, intended to control every aspect of an individual's life from birth to death. Happily, the law has not always been applied to the letter—Islamic civilization would scarcely have emerged otherwise. -Ibn Warraq, Why I Am Not a Musim (Promethius Books); download the whole book for free by Googling ibn-warraq-why-i-am-not-muslim.pdf
State-sponsored central authority which doesn't any papal-like theological pregoratives. I wonder how seriously ordinary Muslims take these state-sponsored scholars of the Middle East?
How seriously? As the Washington Times article cited above suggests, seriously enough to be a troubling and problematic:
"This is not a small-time radical imam trying to stir up his followers with fiery hate speech. This was a considered, deliberate and specific ruling from one of the most important leaders in the Muslim world. It does not just create a religious obligation for those over whom the mufti has direct authority; it is also a signal to others in the Muslim world that destroying churches is not only permitted but mandatory" (Washington Times, op cit).