Cairo — When tall, genial Egyptian Sultan Abou-Ali was studying economics at Harvard University, he was asked to give talks on Islam to other classes. He dwelt on the 1,400-year history of one of the world's three great monotheistic religions, which now includes about 800 million people. He referred to its contributions a thousand years ago to mathematics, algebra, trigonometry, and physics.
''And when I would finish,'' he recalled recently, ''the first or second question was always the same: 'How many wives do you have?' ''
A veil still hangs across much of the Muslim world.
It is broken only by political crisis headlines from Iran to Lebanon, but it still hides Islam itself from Western eyes.
Ask the average North American or European about Islam (the word in Arabic means ''submission'' to the will of God), and the immediate answers will usually be negative - violence, polygamy, or cutting off the hands of thieves.
Muslims are seen as ''fanatical,'' bearded, and either putting up the price of oil or threatening the West's supply lines.
Ask about Islamic history and the answer will often be a pastiche of the Thousand and One Nights, Arab headdresses, Saudi oil sheikhs in shiny Cadillacs, and the decadent opulence of the late Ottoman Empire.
Ask for a description of a Muslim and what you'll get is an Arab or a Turk, even though the bulk of the world's Muslims today live in non-Arab, non-Turkish Indonesia, India, Bangladesh, Pakistan, northwest China, and Soviet Central Asia. Ask for the names of five famous Muslims in history, and you might get two , or three.
Yet the violent pace of events in the world of Islam is forcing the West to look more and more deeply behind the veil.
The events are part of a broad effort by most of the Afro-Asian-Arab third world to find and assert its own identity after two centuries of being dominated by the West and its superior science and technology.
The upheavals that fill the West's newspapers and television screens seem disturbing, restless, militant:
* The Ayatollah Khomeini toppling the Shah of Iran in what remains, despite deeply divided views about the subsequent course of the revolution, one of the few times a Westernized, secular ruler of a Muslim state has been ousted by a mass popular movement rather than the more usual coup or assassination.
* The four-year-old war between Iran and Iraq, threatening Gulf oil lanes, dividing the Muslim world, worrying the superpowers, and sending Iranian teen-agers into battle wearing around their necks metal keys with which, they are told, to ''open the gates of paradise'' after they are killed.
* The assassination of President Anwar Sadat of Egypt by a Muslim extremist in October 1981.
* An attack on the US Embassy in Islamabad the same year.
* The 15 days of fighting in and around the holiest place in all Islam, the Grand Mosque in Mecca in November 1979 when opponents tried to bring down the house of Saud.
* Arabs vs. Israel, including war in Lebanon, and intense Arab opposition to any country acknowledging Jerusalem (the third holiest spot in Islam, after Mecca and Medina) as the capital of Israel.
It can be argued that nationalism and economic self-interest play larger roles in all these events than Islam does.
Yet Islam provides the framework, the basis, for Muslim behavior, just as Christianity remains a reference point of morality and ideals even for those Westerners who no longer go to church.
For Muslims engaged in politics, writes Britain's Edward Mortimer, an Islamic expert, Islam is important because it provides ''the form and the vocabulary ... and can greatly strengthen personal commitment.''
Another British expert on Islam, Godfrey Jansen, says the Afro-Asian struggle against colonialism was in fact an Islamic struggle in Indonesia, Afghanistan, Sudan, Somaliland, Libya, Algeria, Morocco, and west central Africa - and that Islam was one of several factors in Egypt and elsewhere.
''Muslim societies are more openly religious than Western ones,'' says Abdullah Schleifer, a New York Jew who converted to Islam and now teaches social science at the American University in Cairo.
''Although many don't pray at all, and the idea of a pan-Islam movement ended years ago, in their hearts Muslims do tend to see themselves as part of a worldwide Umma or community of believers.
''It is much the same as Christians in the Middle Ages in Europe saw themselves part of something called Christendom,'' Mr. Schleifer says.
Muslims such as Sultan Abou-Ali, now an economics professor in Cairo (and married to only one wife), deplore the West's ignorance about Islam and fear of it since the days of the crusades.
''You define your culture as Judeo-Christian, and you leave out Islam as an enemy,'' he says. ''All of us lose as a result....''
To him and other Muslims, Islam is not to blame for the coups, dictators, poverty, illiteracy, and corruption across the Muslim world: ''We Muslims,'' he says sadly, ''simply don't practice our faith properly.''
To blame the Koran for the Iran-Iraq war, Muslims say, is like blaming the Bible for ''allowing'' the civil war between Christians in Northern Ireland.
But Islam, like Christianity, is a faith used by many people to justify almost any action they care to take.
It also leaves room for traditional, tribal, and ethnic beliefs which predate it. In Indonesia, for instance, which has the largest Muslim-majority population in the world, Islam overlays a basis of mysticism, animism, and village social custom called adat. In Jakarta this correspondent spoke to Western-educated Javanese Muslims who retain faith in precious stones to ward off evil spirits.
Westerners (with the exception of American radio and television evangelists) generally keep religion private and tend to be uncomfortable with the open piety in places like Iran, Pakistan, and Saudi Arabia. Islam to many Westerners is a medieval religious ideology lurking in the poorer two-thirds of the world.
Islam itself, however, makes no distinction between religious faith and the daily human business of politics, economics, and social affairs.
Today, Muslims and Western experts alike are arguing whether a ''revival'' of Islam is under way, one that might conceivably topple more Westernized rulers in the wake of the downfall of the Shah.
There seems a return to the forms of faith - beards, veils, Islamic (interest-free) finance - though whether this is devoutness or an assertion of national, cultural identity in the post-colonial era is hard for an outsider to tell. Presidents Zia ul-Haq of Pakistan, Hosni Mubarak of Egypt, Jaafar Nimeiry of the Sudan, Suharto of Indonesia, and other rulers seem equally uncertain.
In Islam, as in other religions, the ideal and the practice clash. Westerners see the practice and condemn the ideal. Many Muslims deplore the practice and cling to their own concepts of the ideal. Asian Muslims - in Indonesia, for instance - consider their own form of Sunni Islam to be ''purer'' than Islam in the Arab world, which they consider adulterated by oil wealth and materialism.
What are the basics of the Islamic belief?
To the Muslim, Allah (the word in Arabic means ''the God'') made man out of dust, in his human form, and gives him free will to choose between right and wrong. This human being will be judged by Allah on the last day. What the good man does on earth, the Muslim believes, will help him avoid hell and gain a place in heaven.
The Muslim sees much in Islam in common with Judaism and orthodox Christianity. To him, God began to reveal himself to mankind through Adam and continued through Moses, Abraham, and Jesus. All are praised and described in the Koran. All are considered to have preached Islam. The Muslim believes that the Koran is God's final revelation. The word in Arabic means ''recitation.'' The Koran was unfolded, Muslims say, to an Arab trader, father, and leader named Muhammad in Mecca and Medina, via the angel Gabriel, between AD 610-632.
Muhammad, who was illiterate, in turn recited to family and friends, in Arabic. One basic text, the Koran, was fixed soon after his death in AD 632. It is accepted by every Muslim.
The Koran is a long book - 114 chapters (suras) and some 6,000 verses. In all the Prophet used 99 names for Allah - wise, benevolent, merciful, and so on.
To the Muslim, Muhammad is not divine, but the Koran is a divine message. The Koran in Islam is not like the Bible in Christianity. To a Muslim it resembles the role that an orthodox Christian ascribes to the person of Jesus Christ.
To many a Westerner, ''submission'' means fatalism - ''Allah will provide.'' To the devout Muslim, it means subduing the human ego to a constant consciousness of Allah in daily human life. A common phrase in Arabic is inshallah - ''if God wills.''
Like Christianity and Judaism, Islam ackowledges only one God. It agrees with Judaism and disagrees with orthodox Christianity in regarding Jesus as human, not divine, and in denying the existence of the Trinity and the record of the crucifixion.
Muslims call Jesus ''the prophet of mercy.'' They don't believe God became a person or atoned for man's sins on the cross. (One widely held tradition is that the Pharisees and the Romans became ''confused'' and crucified Judas instead.)
Jesus is referred to as Isa ibn Mariam - Jesus born of Mary. The Koran records the virgin birth (and omits any mention of Joseph). It mentions that Jesus healed the lame and restored sight to the blind. Muhammad is not credited with any miracles (except in popular Muslim tradition). The Koran records neither the Ten Commandments nor the Beatitudes. Unlike Jesus, but like Moses and Abraham, Muhammad is seen as a temporal as well as a spiritual leader. He led troops into battle, expanded a city state into a larger domain, and adjudicated disputes.
In the third century of Islam (about the 9th century) scholars codified Muhammad's words as recorded by friends and family into six recognized collections of tradition, or Hadith.
The Hadith are not considered divine - indeed, Muslim scholars concede that they are of varying authenticity.
Some are attested to by three witnesses, some by only one. Together with accounts of his deeds, they form the Sunna, or ''beaten path.''
Hence the name Sunni for the vast majority of Muslims who accept them.
The main Muslim minority is the Shia sect - 80 million to 90 million Muslims living mainly in Iran, Iraq, Lebanon, the Gulf states, Saudi Arabia, Turkey, and Pakistan.
Shias attribute more political authority to their imams (religious leaders) than Sunnis do, seeing them more in the Christian sense of priests.
Shias see their leaders as acting in line with true Islamic authority which, they say, has descended not through the first three imams to succeed Muhammad but through the fourth, Muhammad's son-in-law Ali, and through Ali's son Hussein. They count 12 genuine imams in all.
Hussein, facing greatly superior odds, was killed in battle in AD 680. Shias see him as the ultimate martyr and celebrate his death with intense emotion. They see contemporary imams holding power on earth until the 12th imam returns to earth at a time unknown.
Theologically, Sunni-Shia differences are small. For centuries the division lay dormant. But since 1502 Shias have come to be the majority in Persia (Iran), and the Ayatollah Khomeini is the latest in a long line of politically powerful imams there.
The Koran (accepted by both Sunni and Shia) does not record anything similar to the spiritual account of creation in the first chapter of Genesis. It starts with Allah creating Adam from dust and Eve from his rib. Both were said to have been free from sin.
Allah is recorded as having demanded that his angels bow down to them. One, Iblis (later called Shaitan or Satan) is said to have refused on the grounds that he was made of fire and Adam only of dust. Allah cast Iblis out but granted him the ability to tempt man, and power over all men for all time - unless they believe.
It was Iblis, the Koran says, who persuaded Adam and Eve together to eat the apple from the tree of knowledge. To a Muslim, the devil is very real.
A Muslim sees his human life and belongings as gifts from Allah to be used in God's service and to help others. Suicide is strictly forbidden. So is cremation , since the body must be ''given back to God'' by being buried.
So Islam to a Muslim is both simple (one God, one final prophet) and complex (legalistic, with rules and interpretations for daily life).
It is closer to Judaism than to orthodox Christianity in a number of ways: Jesus not divine, no Trinity, legal scholarship, dietary laws.
It agrees with orthodox Christianity on the existence of an afterlife and a final judgment, but believes that Jesus was not resurrected but simply taken into heaven by God.
In Sunni Islam, an imam is simply a learned man who may lead prayers on Friday (the Muslim Sabbath). Imams make no intercession with Allah for man, though Shias believe they do.
''For we Sunni, it's direct dialing (to God),'' says Pakistani official Shafaq Hashmi. ''The Shia goes through the operator.''
So Islam is conservative and traditional, putting family above all other human ties - but to many younger Muslims it is also a revolutionary alternative to Western and Eastern cultures. Islam is communal, ritual, and austere - though practiced with passion by Shias, and by many Sunnis who follow individual teachers in brotherhoods known as Sufi.
''Islam seeks to balance between the material and the spiritual, which are equally important to give humans equilibrium,'' says Egyptian Nabil Osman.
The five basic pillars of Islam, followed by almost all Muslims, are:
1. Oral declaration that there is one God and that Muhammad is his prophet.
2. Praying five times a day, at dawn, noon, late afternoon, sunset, and early evening.
3. Fasting during daylight for the 30 days of Ramadan.
4. Making a pilgrimage at least once during one's lifetime to Mecca and its focal point of the kaaba, (a cube-shaped monument 50 feet high, thought to have been built by Abraham and Ishmael, now covered with black and gold hangings).
5. Paying zakat, an alms tax of 2.5 percent of savings each year to the poor.
Each pillar has inner meanings. Millions of Muslims know them (fasting is purification and obedience, while many say the real kaaba is the human heart). Millions more simply observe the outward forms.
Next: The Principles and Practice of Islam. .