London Times correspondent Mortimer, stationed in the Middle East since 1973, confesses that he was as baffled as anyone else when the Shah of Iran was toppled by crowds shouting ""God is the Greatest""--and this top-notch exploratory work is the result. In the first third, Mortimer sets out ""to discover in what ways political problems look different to Muslims, and why."" (Good-bye, then, to the Western ideologies that long colored our view of Middle Eastern politics.) Tracing the development of Islam from the community of believers founded by Muhammad (""from the beginning, what we would call a state""), Mortimer shows that revolution, to restore a truly Islamic order, was an ever-present prospect. Examining the historic divisions of Islam, he identifies the sources of revival movements, including the ""fundamentalist."" Moving into the modern era, he describes the Muslim feeling ""that their world was in decline""--and, as the Muslims confront predominant Western power, he identifies two key responses: protective emulation and unified resistance. The second, larger--and up-to-the-minute--part of the book examines ""the role played by Islam. . . in the politics of six modern societies."" Here is Turkey, caught between Ataturk's reforms and Muslim activism; Saudi Arabia, where the Koran is the Constitution (except, explosively, behind closed palace doors); Pakistan, a self-described ""ideological state"" in search of an Islamic identity; ""Arab Nationalism and Muslim Brotherhood""--in, most prominently, the Libya of ""fundamentalist""/modernist Qadhafi and the Egypt of Sadat. Remaining are Iran and--with the question ""Is the 'Islamic revolution' likely to spread northwards?""--the Muslims in the USSR. (In the offing, perhaps: ""a Muslim equivalent to what has been happening in Catholic Poland."") Islam, Mortimer concludes, is what individual Muslims believe it is--""and they are by no means in agreement on its political, social and economic content."" (That it has such a content will be news to many.) Brisk, searching, and totally unpresumptuous: an exemplary work on a demanding subject.