As Shadi Hamid, a fellow at the Brookings Center for Middle East Policy, put it in an Atlantic article entitled "The Roots of the Islamic State's Appeal": "ISIS draws on, and draws strength from, ideas that have broad resonance among Muslim-majority populations. They may not agree with ISIS's interpretation of the caliphate, but the notion of a caliphate — the historical political entity governed by Islamic law and tradition — is a powerful one."
In other words it's consistent with all the polls of Muslims both in the west and in Muslim-majority countries (see "Islam in figures" above): they may not all agree with killing and mayhem, but they agree with the main aims which are at the core of Islam: the universal imposition of Sharia law and an Islamic caliphate (a theocracy) for the whole world. Many (most?) Muslims may prefer for this to be done peacefully by the "religion of peace", but if necessary violence will do.
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