Behind the columns along the National Museum's Gallery of the Alphabet, where tablets 12 centuries old were once exhibited, crude cinder-block walls divide the space into stalls for sleeping soldiers. Abandoned blankets, clothes, boots and car batteries lie around the dank, cavernous interior, bare except for large blocks of concrete said to encase valuable sculptures. Huge windows that once illuminated the now-removed or looted exhibits are filled in with sandbags. Spilled dirt and trash cover the floors.

Beirut's museum is now a different sort of tourist attraction. Captured by Israeli troops in heavy fighting 10 days ago with Palestinian and Syrian forces, the colonnaded building -- closed for most of the past seven years -- has been reopened to demonstrate what the Israelis say are its foes' abuses of Lebanese civilization.

Long the main landmark along the no man's land dividing East and West Beirut, the museum was the first stop on a trip today through the front lines at two main crossing points between Israeli- and Palestinian-controlled sectors of the capital. The tour showed that despite eight days of heavy fighting since a major Israeli thrust gained a few hundred yards Aug. 4, no significant advance has been made.

Practically all there is to show for the intensive, almost non-stop pounding by Israeli warplanes, tanks, artillery and gunboats is mind-boggling physical destruction: shattered buildings, smoldering ruins, fallen trees, streets strewn with shrapnel and debris.

The tour also capsulized the complexity of the Lebanese fighting. Within a distance of about 300 yards west of the museum, a British reporter and I came across a gamut of armed factions. Wending our way along back streets and dirt paths through a maze of bombarded buildings, backyards and vacant lots -- the new way across the dividing Green Line -- we encountered Israeli troops, their Christian Phalangist allies, Lebanese Army regulars, remnants of a Syrian brigade, Palestinian guerrillas of the Saiqa and Palestinian Liberation Front factions and Lebanese leftist militiamen from the Murabitoun and Parti Populaire Syrien parties.

A dog leg of not more than 50 yards between abandoned apartment blocks separated Israeli troops from their nearest foes, a group of youthful Murabitoun militiamen. Seemingly oblivious of each other's presence, so close but out of sight, the Israelis lounged beside a few tanks and armored personnel carriers tucked behind buildings and in narrow alleys, while the flak-jacketed Lebanese leftists casually waved a trickle of people through their checkpoint in both directions.

Lebanese civilians, many carrying suitcases or bundles of belongings, took advantage of the day of calm to file out of besieged West Beirut to the predominantly Christian east. But many other Lebanese also crossed the lines in the other direction, some of them to inspect houses or apartments they had vacated in the mainly Moslem west.

In the museum, which the Israelis formally turned over to its pre-war Lebanese curator on Tuesday, Israeli soldiers mingled with Lebanese Army regulars who have brought in cots and other gear. Israel charged that the museum had been "commandeered by the Syrian Army and Palestine Liberation Organization terrorists who used it as a fortified base and barracks."

One of the Israelis inside the museum, a lieutenant originally from Liverpool, England, said the heavy shelling near the crossing had been necessary to protect Israeli troops. Wearing a bush hat, round glasses and several days growth of beard, he added a reservation in a thick Liverpudlian accent.

"One thing I learned in modern history is that you can't destroy guerrilla movements with conventional warfare," he said. "All we're doing is buying time."

A couple of hundred yards away, a fighter from the pro-Syrian Saiqa group said the Israelis had tried to advance under covering fire from tall buildings, but had been unable to gain much ground. Wearing jeans, a vest and a cowboy hat with a skull-and-crossbones patch, he also said he would obey an order from his superiors to stop fighting and leave Lebanon.

A fighter from the leftist Palestine Liberation Front echoed his sentiments, but said, "We won't leave until we know our civilians who stay behind will be protected from the Phalangists and from the Israelis." He said the Palestinians were counting on the arrival of a multinational peace-keeping force for this protection, and that in any case, they would make sure they left their Lebanese leftist allies well armed.

Ahmed Debeybo, a 60-year-old regional distributor for Lebanon's Pepsi-Cola plant, took a somewhat dimmer view of this prospect.

"They're all hoods," he spat out as a jeep full of leftist fighters drove by. "And the Palestinians are worse. We've suffered for seven years. Perhaps the cause of the Palestinians is just, but their leaders are no good."

Standing in front of a candy shop that seemed to have survived with only broken windows, he said he desperately wanted the Palestinians to leave. "It's what we all hope. We're counting the minutes."

But a Lebanese housewife, going back to West Beirut to inspect her apartment, disagreed. "This is not the Palestinians' fault," said Salwa Baydoun. "They're all bad. The Israelis, the Arabs, the United Nations. Everybody is watching the Lebanese die."

All around, buildings had been scored by shells and rubble littered the streets. The shells apparently came from every direction, including from gunboats lying offshore to the west and firing all the way across Beirut.

A bit farther down the street, the Rue Koleilat, a five-story apartment building had been reduced to a mound of blackened, smoldering rubble. Debeybo, who fled the neighborhood temporarily three days ago, said it had been hit by two shells from gunboats and had burned down because there was no water to put out the fire. On the sidewalk across the street from the ruins lay a dead rat, possibly killed by the concussion.

Despite the damage, Debeybo said he planned to return to his apartment this week. "We feel it is over," he said. "We hope so anyway. We can't believe it could get worse than this."

As he spoke a burst of machine-gun fire reverberated from the direction of the racetrack a few blocks to the southeast.

On the way back to East Beirut through the Gallerie Semaan, another main crossing point between the two sectors, about 200 cars were backed up waiting to leave the besieged West. They ranged from Mercedes and Fleetwood limousines to battered taxis and pickups, and their passengers came from all walks of life. Many cars had mattresses and other belongings piled on the roofs. One contained cages full of canaries.

A few yards beyond an Israeli checkpoint, Phalangist militiamen brusquely herded the refugees into lines, first to check their identities, then to examine their belongings.

At a nearby traffic circle, hundreds of people milled around, many having been stopped by the Phalangists and Israelis from crossing back from east to west. Militiamen fired rifles in the air to break up arguments and disperse loiterers.

For whatever reason, a massive traffic jam clogged the road from the circle a few miles down a hill into East Beirut. Among the vehicles stuck in it were dozens of Israeli jeeps, trucks and armored cars.