Islam past, present, and future; Militant Islam, by G. H. Jansen. Boston: Harper & Row. $8.95.

Ayatollah Khomeini has had Westerners scurrying around for the past year trying to learn more about Islam. Islam, of course, has been a force on this planet for the past 1,300 years, with Muslims the second-biggest religious denomination on earth, after Christians. But it has taken the turmoil of the past 18 months in Iran to jolt people in the Western world into trying to discover what Islam is and what has provoked its current "militancy." G. H. Jansen's "Militant Islam" provides a lot of answers.

Jansen is a gifted and fluent writer, the Levant correspondent of the respected London weekly, The Economist. Of Anglo-Indian stock, he dedicates his book to his daughter by his American-born Muslim wife.

Although Jansen's current base is in Cyprus, he spends most of his time in the Muslim lands of the Middle East. His earlier writings have shown him to have particular insights into third-world thinking, and they serve him well in this book.

Here he offers in lively, readable form a broad yet appropriately detailed overview of Islam, past, present, and future. Jansen is right in saying that Islam has a special appeal in the third world, but some may wonder if he is not going too far when he asserts that "without Islam the Afro-Asian movement would probably have aborted." There are other assertions open to challenge. Yet this does not detract from the overall value of the book.

"Militant Islam" should help to redress prejudiced perceptions handed down from generation to generation in the West, from the Crusades through the Ottoman incursion into Europe to the often biased post-World War II reporting on and from the Middle East.

Of course, the prejudices exist on both sides. To many Muslims, the Christian record is just as questionable as the Muslim record is to Christians. But whatever clinical assessment may be made of either, the fact is that each of the two -- Christendom and Islam -- has reached high points of achievement as each has developed an improved monotheistic concept of God.

Islam's greatest contribution to civilization to date came immediately in the wake of its Prophet, Muhammad. He conveyed, initially to his fellow Arabs, a startlingly clear concept of the uncluttered one-ness of a universal God and of the redundancy of the need for any medium between God and man. With that, Islam was off -- conquering from the Atlantic to the western edge of China. And not only conquering but contributing to human progress in the fields of mathematics, the natural sciences, astronomy, and navigation. Those who doubt it should recall the Arabic root of such words in English as "algebra," "alchemy," and "admiral."

But all this was overtaken by a subsequent explosion and elevation of thought within Christendom -- the Renaissance. From that flowed the European establishment of empire around the globe, including most of the Muslim parts of it. From that flowed, too, first the industrial and more recently the technetronic revolution (as President Carter's national security adviser, Zbigniew Brezezinski, has called it).

But World War II and its aftermath has seen the end of overseas European empires, the re-emergence of Muslim peoples from foreign colonial rule -- and the despairing cry in the Western world that "God is dead." As Jansen rightly points out, that cry is almost inconceivable within Islam, except perhaps from the so-far-insignificant handful who have turned their backs on traditional religion in favor of atheistic "scientific socialism" as purveyed from Moscow and elsewhere.

In many ways Christendom has made a better job of adjusting to material progress in this modern age. Indeed, Christendom is for the most part the begetter of that progress, the direct consequence of the Renaissance. But in the process it has tended to lose conscious sight of God. Islam, left behind in the record of material progress, has clung to its concept of God (which to many outsiders seems very much out of touch with the world of this last quarter of the 20th century). As this reviewer sees it, both Christendom and Islam are in fact faced with the same basic challenge: reconciling traditional concepts of God with what both see happening around them. Perhaps the question should be asked (and Jansen does not pursue this line at all): Is this in any way possible , if men of either faith stick to those traditional concepts?

Still, Jansen will set unprejudiced non-Muslim readers thinking. He and his publisher have done an impressive job in getting out an informative book in a very short period of time. For an enterprise so speedily completed, this reader noticed only a few slips. For example, Egyptian President Gamal Abdel Nasser did not execute but commuted the capital sentence pronounced on the Muslim Brotherhood leader, Hassan al-Hudaibi, after the assassination attempt of 1954. And Ali Shariati, whose teachings are so influential in today's Iran, died in 1977, not 1975.

Jansen might irritate some readers with his opinionated asides. To quote only two: the Beatles produced "half a dozen songs that will last as long as the hundreds produced by Schubert"; and "two recent examples of promotion beyond the level of competency are the US General Westmoreland in Vietnam and Field Marshal Montgomery in World War II."

Even his judgments tend occasionally to be overopinionated. Here are some examples:

* "One can speak with certainty of the eventual ousting of Sadat."

* "For wholesale imitation to succeed, the imitators have to be very clever and hardworking, which the Japanese are and the Turks are not."

* "The Kemalist Lilliputians tried and failed to tie down the Islamic giant."

* "The Tunisians to this day are genuinely pleasant people, surprisingly different from their neighbors, the Algerians and Libyans."

One wonders how Mr. Jansen's Turkish, Algerian, and Libyan friends are going to take this.