Shortly after the Reagan administration made the dramatic announcement that it would begin talks with the Palestine Liberation Organization, the State Department issued a secret alert to American diplomatic and military facilities overseas, warning about the potential of a new rash of terrorism.

"Every past peace process has coincided with new violence. Since the stakes are even higher this time around," said a Reagan administration official, "it is more than likely that someone will try to do something even more sensational" - probably a PLO splinter group.The alert underscores a crucial fact about the powerful organization with which the United States will at last be negotiating: Whatever else it is, the PLO is far from monolithic or cohesive.

Since it was established at an Arab summit in Cairo in 1964 as a puppet group largely controlled by the late Egyptian President Gamal Abdel Nasser, the organization has evolved into a multifaceted and sometimes bitterly divided conglomerate, with factions embracing sharply different attitudes, approaches and methods.

So deep are some of the divisions among the Palestinians that Arafat himself may now become a target of the kind of brutal terrorist attacks that have been the hallmark of his organization.

And the PLO's internal divisions, coupled with its tradition of violence, pose a tough challenge for the United States as it tries to use the new talks to move toward a settlement of the Mideast dispute.

The six factions now under the PLO umbrella vary widely in political orientation, from democratic to Marxist. Their choice of Arab allies is equally disparate, ranging from relatively conservative Saudi Arabia to militant Syria. The world's most notorious guerrilla movement also contains within it a host of legitimate business enterprises and financial assets that make it a leading Third World multinational business concern.

Inspired by the Algerians' uprising against the French in 1962, the PLO was originally formed to enable Palestinians "to carry out their role in liberating their homeland and determining their destiny."

In 1964, that meant retrieving the land on which the fledgling state of Israel was created. The West Bank and the Gaza strip had not yet been lost.

The first PLO chairman was Ahmed Shukairi, an ally of Nasser. Arafat, at that point, was far from the scene.

He was affiliated with Fatah, which means "conquest" or "opening" in Arabic. It had been formed in 1959 by five young Palestinian activists whose first big venture was publication of a magazine addressing Palestinian political and social issues.

Arafat, a Cairo University engineering graduate, was elected its first chief. Lebanese politicians love to recall how he used to peddle the magazine door-to-door in Beirut in the early days.

While the PLO sat in the conference halls of Arab capitals, Arafat's Fatah began forming a guerrilla organization to back its words with action. It issued Military Communique No. 1 on Jan. 1, 1965, claiming credit for a notably unsuccessful attack against Israel.

The Palestinian movement in general, however, did not pick up momentum until the 1967 Middle East war, when Israel captured large chunks of Egypt, Jordan and Syria - plus sacred East Jerusalem. Thousands of new Palestinian refugees were galvanized into action, coalescing into several new groups.

By 1969, Arafat's Fatah had emerged as the most powerful of these. In what was to be the first of several masterful political maneuvers, he manipulated a takeover of the PLO leadership. The various other groups, some with open reluctance, then fell in with the PLO.

Daring guerrilla assaults across Israel's borders and spectacularly bloody terrorist acts quickly became the PLO's trademarks.

Among them were the 1970 triple hijacking of American, British and Swiss airliners, later blown up in the Jordanian desert, and the 1972 seizure of Israeli athletes at the Munich Olympic games. Eleven Israeli hostages and five Palestinians were killed.

The wave of terrorism produced revulsion in many parts of the world, but in the desperate calculus of the PLO guerrillas it had the desired effect: The outside world began paying attention to the Palestinian issue. Western nations began pressing the PLO to look for diplomatic alternatives to violence.

Ironically, peace has always been Arafat's most troublesome problem.

Two rounds of splits within the movement, in the early 1970s as well as in 1982-83, produced hard-line factions that were outside the PLO mainstream and rejected diplomacy.

Both splits serve as ominous precedents for the current PLO-U.S. dialogue, because both were largely the result of moves by Arafat on the diplomatic front - moves tied directly or indirectly to the United States.

Among the so-called "rejectionist front" are the Palestinian factions best known for conducting terrorist attacks outside Israel. Abu Nidal, whose faction is based in Libya, was responsible for the attacks on the Rome and Vienna airports three years ago that resulted in more than 20 American and European deaths.

Abu Nidal's Fatah-Revolutionary Council was also linked with the hijacking of a Pan American flight in Pakistan and an attack on a synagogue in Istanbul, both in 1986.

The attacks and threats have not been limited to Israelis and Americans. After Abu Nidal, whose real name is Sabry Banna, split from the mainstream PLO in the early 1970s, his group tried Arafat in absentia and sentenced him to death.

Arafat was charged with treason for betraying the struggle when he began pursuing diplomatic solutions. His effort resulted in his first United Nations address in 1974 when he waved an olive branch at the General Assembly.

"I have come bearing an olive branch and a freedom fighter's gun," he said. "Don't let the olive branch fall from my hand."

The second split followed Israel's 1982 invasion of Lebanon and Arafat's agreement to a U.S. plan to pull his fighters out of Beirut in order to end the massive bloodshed.

His controversial decision to abandon the struggle and his loyalty to commanders who had performed poorly - some charged they had fled combat with Israeli forces - triggered a backlash.

Abu Moussa, a former Arafat lieutenant whose real name is Said Moussa, and other pro-Syrian factions defected from the PLO. In 1983, with Syrian military assistance, they launched an offensive against Arafat loyalists in the northern Lebanese port city of Tripoli.

Weeks of fighting resulted in hundreds of Palestinian deaths - for the first time at Palestinian hands. Arafat was also once again forced to abandon Lebanon.

The split was the deepest and longest in the PLO's history. It was only partially healed at a Palestinian summit in Algiers in 1987.

The six factions now under the PLO umbrella are still far from united on either the peace process or the form of a Palestinian homeland. "The alliance is, at best, tenuous," said a State Department official.

But the PLO is not just a political movement. During the 1970s, its various wings also developed social and business outlets that amounted to a mini-government.

PLO industries, often referred to jokingly in Beirut as "PLO, Inc.," include factories that make furniture, clothing, handicrafts and other basic goods. The concept developed when Palestinian refugees found employment opportunities limited.