From beneath the still falling Israeli shells and the debris of its headquarters and training camps in and around the Lebanese capital, the Palestine Liberation Organization has begun to assess what it has lost during the Israeli invasion, as well as what remains intact.

The losses have been heavy, including enormous amounts of weaponry and much of the terrain that had been established as "independent" Palestinian turf in the south.

The PLO also has lost, at least temporarily, control over the overwhelming bulk of the perhaps 400,000-strong Palestinian community living in Lebanon, as well as many fighters trained in the use of sophisticated weapons.

But the Palestinians' misfortunes look less grim in the light of Israel's failure to achieve what it was presumed here were its objectives--the destruction of the PLO leadership, the departure of the Syrian army from Lebanon and the installation of a new Lebanese political order more acceptable to Israel.

At the same time, PLO Chairman Yasser Arafat, who knows that over the years he has achieved more politically and diplomatically than through the armed struggle to which he feels obliged to pay lip service, appears to have managed yet again to transform military defeat into at least temporary political survival.

Ironically, it was Israel's expansion of its original aims in Lebanon--or at least the belief here that its goal was far more extensive than the initially claimed desire to push the Palestinians back 25 miles from the border--that worked in Arafat's favor. Israel's failure to stop in southern Lebanon assured at least in part the eventual support of other Arab nations, and provoked international pressure on Israeli Prime Minister Menachem Begin, leaving Arafat free to claim something of a diplomatic victory among his shell-shocked comrades.

In publicly telling the Syrians to stay out of its fight with the Palestinians, Israel made it practically impossible for Syrian President Hafez Assad to do so.

With Israeli armored columns threatening to cut off the Syrian Army's lines of communications along the vital Beirut-to-Damascus road, Israel's warplanes then destroyed Syria's missile sites in the Bekaa Valley.

The Syrians, who had begun pulling out of Beirut and were thought by the Palestinians to have betrayed them, then felt obliged to send back first-line units and fight. "They helped us a lot," one Palestinian official said.

The Israelis further clouded their image of invincibility, in the minds of people here, by dropping leaflets on Beirut boasting, "We shall capture the city in a short period."

No matter how shaky the Syrian-Israeli cease-fire proves, when it was announced today the threatened Israeli ground assault against Beirut had been dropped and the Syrians were still not totally uprooted from the capital.

Nor did the Israelis' understanding of the complexities of Arab--especially Lebanese--politics show much sophistication. The Israelis had worked hard and long to turn one segment of the Lebanese population after another against the Palestinians.

But far from abandoning the PLO, the guerrillas' increasingly restive Lebanese and Syrian allies have rallied round in opposition to the invader after months of on-again, off-again warfare caused by the slow erosion of the Palestinians' popularity.

Still barring yet another change of military fortunes, Israel's allies among the Christian Maronite community have been embarrassed by the course of events and had to refrain from acting on their dream of sending their militiamen to join up with the Israelis.

The captured weaponry can be easily replaced, as lost arms were after every major Palestinian military defeat--beginning with the PLO's ouster from Jordan in 1970 through their damaging participation in the 1975-1976 Lebanese civil war, the smaller Israeli invasion in 1978 and the two-week conflict with Israel last July.

Perhaps to keep up their courage, Palestinian officials are now trying to look on the bright side of what has happened.

They claim to have lost no high-ranking commanders or other officials and apparently to their surprise managed to keep in touch with entire units, even of battalion size, that were either isolated or side-stepped in the Israelis' rush north.

Yet the trickiest part lies ahead, for without a formal cease-fire between the Palestinians and Israelis each side is determined to inflict maximum casualties on the other.

The Israelis are over-extended, according to military specialists here. But their big batallions still threaten the Palestinians, who prefer to make Israel fight a guerrilla war.

Palestinian officials admit privately that they count less on their military prowess to force the Israelis to withdraw than on the late-starting Saudi and Egyptian-led pressure on the United States to prod Israel to accept a cease-fire.

"Things looked pretty grim until two days ago," a Palestinian insider said. He explained that aside from renewed faith in their own abilities, the Palestinians then began seeing some diplomatic support that had been lacking.

"Initially lukewarm, the pro-American Arab regimes began realizing their stability was at stake because their own people saw them as weak and despicable," he added.

Particularly telling for the conservative regimes was the U.S. veto at the U.N. Security Council preventing condemnation of Israel's invasion.

In the Palestinian game of survival everything helps. But a Palestinian official conceded, "We are still up against the wall."