The Arabian-American Oil Co., the world's largest oil company, and the backbone of the longstanding U.S.-Saudi relationship, appears to be emerging from 47 years of American domination as the exception to the image of multinationals in the Third World as merely selfish plunderers of its wealth.

Now fully owned by the Saudi government, the giant of giant oil producers that once took the brunt of local criticism for rapacious exploitation of resources is taking on another reputation as a highly successful transmitter of Western technology to Saudi society and a mainstay of the country's industrialization effort.

It is also playing a leading role in the education of Saudis barely able to read and write for highly technical jobs and management skills badly needed throughout the kingdom, particularly in Aramco.

Seldom does one hear a kind word about multinationals anywhere in the Third World, either by local governments or citizens. But Saudis inside and out of Aramco can be heard praising its record, even that made while it was still a privately held company, despite signs of a lingering resentment among university students.

"I have a very positive view about Aramco despite years of exploitation," Fuad Farsi, deputy minister of industry, said in an interview last year. "The diffusion of technology has been good through it."

"If the public didn't like Aramco, then the government would have gotten another company," remarked Abdulaziz Hokail, its vice president in charge of training, as he discussed the variety of tasks the company has been asked by the government to take on throughout the Eastern Province, the kingdom's oil heartland.

While a Supreme Petroleum Council headed by Crown Prince Fahd makes all the key decisions on production and investments, Americans continue to staff top posts in the company and the four old owners--Exxon, Mobil, Socal and Texaco--to provide personnel and know-how.

Both the president and the board chairman of Aramco are still Americans, the majority in all levels of top management are still Americans and perhaps most symbolically of all, the name of the company nearly two years after the Saudi takeover is still the same. In fact, the final formalities of the Saudi takeover have yet to take place.

The special relationship apparently serves both sides. The government is assured of the most advanced oil technology and expertise it wants, while the former owners get around 65 percent of its production--the cheapest high-grade oil on the world market.

Aramco, meanwhile, remains the keystone of the Saudi economy. Not only is it the kingdom's major producer of oil and revenues on the order of $100 billion annually, it is also responsible for building and running its multibillion-dollar Master Gas System.

This will end the wasteful flaring of natural gas associated with the oil and process 2 billion to 3 billion cubic feet of it daily, for use in the complex of industries going up in nearby Jubail and at Yanbu on the Red Sea.

In addition, the company has been put in charge of building a 1,600-megawatt electricity plant north of here at Ghazlan, producing power for the entire Eastern Province, building a 250,000 barrel-a-day domestic refinery and a 730-mile gas pipeline to Yanbu as well as exploration for new oil reserves.

On the later score, Aramco has succeeded in finding each year more recoverable oil reserves than Saudi Arabia produces in a year. Already, the kingdom accounts for more than one-quarter of all the known reserves throughout the globe, about 178 billion barrels in 1980.

Aramco is so big that it long ago set up its own schools to educate thousands of Saudis. Yet its recent expansion of industrial activities has required a major expansion in this area.

Last year, Aramco hired 5,000 more Saudis, only 240 of whom were college graduates, while 2,500 held only ninth-grade degrees. The company pays the latter to complete their education and sends about 400 of the best students to the United States for master's degrees in engineering every year, according to Hokail, the vice president for training.

He said that by 1986 Aramco plans to have 5,500 Saudis on college scholarships either here or abroad. John J. Kelberer, Aramco's American president, estimated that by the middle of this decade the company might be spending a third of its budget on training and educational facilities.

One example of the way Aramco has transformed semi-educated Saudis into top management personnel is Abdullah Saif, who is general manager of Aramco's vast complex of collecting, processing and pumping plants at Abqayq, 50 miles southwest of Dhahran.

Over a luncheon with a dozen Saudi and American assistants, Saif explained how he began with Aramco 20 years ago with only a ninth-grade education. His first job was as a part-time clerk, while he went to an Aramco high school. Then he was sent to the University of Oklahoma for a science degree.

He said there was no attempt at forcing the pace of Saudi promotion within the company, commenting "we never push someone just because he is Saudi faster than he should go."

One of the great achievements of Aramco, according to Saif, has been the introduction into the kingdom's easy-going work habits the notion of an eight-hour day.

"Elsewhere, it is six hours officially," he said. "We have been able to compromise on many things except the eight hours."

In return, Aramco offers better fringe benefits than the government or most other companies, including 20 percent to 30 percent higher pay, generous loans and free land for homes, medical care and various bonuses.

The shortage of skilled labor and the continuing expansion of Aramco activities in the kingdom will probably make it impossible for the government ever to "Saudi-ize" the company fully.

Hokail said Saudis now constitute 54 percent of Aramco's 56,600 employes, 41 perecent of all unit heads, but 85 percent of the oil and gas operators. The company still relies very heavily on foreigners for maintenance. "We have a lot of training to do still," remarked Hokail.

Company figures show that in October, there were 4,776 Americans working for Aramco, an increase of 456 over the year before. Other nationalities make up the rest.

Kelberer attributes part of Aramco's success to the fact that it was set up as a separate Delaware-based company with its own organization, interests and personnel. It put down roots in the kingdom early, and by 1952, before the oil producers had begun to apply pressure, it had already established its heaquarters here.

Unlike expatriate attitudes in most other Third World oil-producing countries, many Americans took a real liking for the kingdom, despite the rigors of its climate and traditional Islamic regulation of mores, which included bans on alcohol and public amusements.

There are 120 to 140 second-generation Aramco families and a few third-generation ones, according to Ahmed Lughod, a public relations official. Kelberer has lived here more than 30 years.

The origins of Aramco go back to 1933, when Standard Oil of California (Socal) signed an agreement with the kingdom for prospecting. In 1936, Texaco joined the venture, and then in 1944 the two gave the company its present-day name.

Oil was first struck in December 1936 at a well called Damman No. 7. After the extent of the bonanza and the cost of exploiting it became known, the two original American partners in 1948 cut in two others, Standard Oil Co. of New Jersey, now Exxon, and Socony Oil Co., later renamed Mobil.

Mobil obtained a 10 percent share and the other three 30 percent each.

The Saudi takeover began in late 1972 when the oil minister, Sheik Ahmed Zaki Yamani, first applied his relatively moderate theory of government "participation," as opposed to outright nationalization, to obtain a 25 percent interest. Two years later it increased to 60 percent.

Negotiations for a total takeover were completed by 1977, but the Saudis' easy-going attitude seemed to be summed up in the fact that it did not take effect until three years later.