Alevis muslims do not meet in Mosques but rather in meeting houses. Their core beliefs include love and respect for all people, tolerance towards other people and religions, and respect for work. They make up a large minority of Muslims in Turkey. An article in this weeks Time Magazine says the following about a meeting of Alevis:
Most noticable were the girls without headscarves flirting with boys in the entrance hall. Then there was the laxity: with no call to prayer ringing from loudspeakers, worshippers straggled in late, while one of the religious leaders joked about having to compete with TV sitcoms.
We are not talking about a small number of people in the Alevis sect. Fifteen to thirty percent of Turkey's population are Alevis. Alevis make are the 5th or 6th largest religion in the world with around 10-20 million members. Believe it or not they are an offshoot of Shi'ite Islam, but believe in incorporating piety and modernity into their faith-based humanism.
The origin of Alevism is controversial. It may even pre-date Islam, having taken on a veneer of Shia theology. Alevis in Turkey have had to disguise themselves as Sunni Muslims to avoid persecution - that is, until recently. A nice little summary of Alevism can be found here or a more detailed discussion here.
So now we find that the simplistic division of Muslims into the Shia and Sunni categories is just that - simplistic. In the Time Magazine article, Alevi leader Muharrem Ercan says "We solved the issue of whether Islam could be tolerant 750 years ago".
The average person in the Western world still has much to learn about Islam.