On Sunday last, June 6, Israeli armed forces moved in substantial force into the southern part of Lebanon. Their assigned goal according to Israeli official announcements was to push PLO forces 25 miles farther north and hence beyond artillery range of Israeli settlements.
At the western end of the Israel-Lebanon frontier a distance of 25 miles would put the new Israeli military frontier about half way up the coast from Israel itself to the Lebanese capital of Beirut. At the eastern end of the frontier another 25 miles beyond the Golan Heights (which Israel claims to have annexed) would put Israeli forces astride the main highway over the Lebanon mountains which connects Beirut with the Syrian capital of Damascus.
Israeli forces could not occupy and hold any part of that main east-west highway without having to fight for it with Syrian troops who use it. It is the main supply line to Syrian forces in and near Beirut. An Israeli position even near this highway would endanger all Syrian forces on the west side of the Lebanon range of mountains and thus the Syrian position in Lebanon.
This latest outbreak of fighting between Israel and the Arabs is the climax to a series of events dating back tk last July.
On July 17 Israeli jets bombed several modern apartment buildings in the heart of Beirut killing 300 and wounding some 800 persons, most of whom were said to be civilians. Israel said its purpose was to knock out PLO headquarters in Beirut. Opinion worldwide was shaken by the severity of the action. President Reagan sent his special Mideast expert, Philip Habib, to the area. He succeeded on July 24 in obtaining a cease-fire from both Israel and the PLO forces.
The July 24 cease-fire brought about a gradual subsidence of hostilities. By October fighting had in fact stopped. But tension continued. There were repeated reports of the massing of Israeli troops along the frontier in preparation for an invasion. On Nov. 9 Israeli Defense Minister Ariel Sharon declared that he ''was not going to leave this situation forever.'' He presumably meant the existence of PLO forces within range of Israel's frontier. On Nov. 14 the PLO's Yasser Arafat ordered PLO mobilization due to continued reports of pending Israel action.
On Dec. 14 Israel did act, but not by invading Lebanon. Instead it announced that it had extended the application of Israeli law to the Golan Heights. This was tantamount to annexation. The UN Security Council, with the US concurring, called Israel's annexation ''illegal'' and threatened ''appropriate measures'' unless it was rescinded. It was not rescinded but it has not been recognized as valid by any outside country.
There continued to be reports of impending Israeli troop movements northwards. In early January President Reagan sent a message to Israeli Prime Minister Begin urging him to take no such action. On Jan. 19 Mr. Begin wrote a letter to the President promising no invasion without ''clear provocation.''
There was no ''clear provocation'' or provocation of any kind by the Arabs through January, February, and March. But there continued to be Israeli troop movements along the frontier. On April 9 the US State Department in Washington took public notice of such Israeli troop movements and urged ''utmost restraint'' on both sides.
On April 11 an Israeli soldier in uniform ran amok in the Muslim Dome of the Pock Mosque on Temple Mount in Jerusalem. Two Arabs were killed, several others wounded. Arabs rioted all through Israel and in Israeli occupied areas. In one of those riots an 8-year-old Arab child was killed in a fusillade of Israeli bullets.
On April 21 an Israeli soldier was killed by a land mine planted in an area in south Lebanon controlled by Israeli forces an area known as Haddadland after Major Saad Haddad who leads Arab forces in the pay of Israel. Within hours Israeli jets broke the nine-month truce. They came in from the sea and out of the setting sun against PLO centers along the coast south of Beirut.
The PLO responded with anti-aircraft fire, but did not take reprisals against Israel's own territory.
On May 9 Israeli warplanes again bombed and strafed PLO villages along the Lebanese coast in alleged retaliation for land mines said to have been found inside Israel and for a bombing on a bus in Jerusalem.
This time the PLO forces did retaliate by sending about 100 rounds of artillery and rockets into Israeli territory. No Israeli casualties were reported. Yasser Arafat said he would renew the truce if Israel refrained from further hostilities.
That brings us to the present. Last Thursday, June 3, Israel's ambassador to Britain was shot and critically wounded as he came out of a London hotel. The PLO denied any complicity. But the next day waves of Israeli jets struck the same PLO villages and centers along the Lebanon coast. This time the PLO did respond with artillery fire along the frontier. And this time the Israelis attacked again by air and sea and also sent their tanks into Lebanon. The Israeli invasion which Mr. Sharon has apparently wanted since last summer was unleashed.