The boy has tousled brown hair, a sparse beard and gray eyes, and is dressed in a faded Indian tunic and the customary blue jeans of Italian students.

He is 20 years old, and the cowhide shoulder bag he is wearing is the same one he carried during riots here last March to protest the killing in Bologna of a leftist student.

Today the bag contains two paperbacks, some fruit, a wallet, a comb and the keys to his motor-scooter. On the the night of March 12, it held rocks, a length of chain and the makings of two Molotov cocktails.

Later in the evening, there was space for the three pistols he stole when he participated in an assault on a sporting goods store with other leftists. Except for some target practice in the country, he was not used the guns since, but he is keeping them since he "might need them some time soon."

A political activist and a sympathizer of Italy's increasingly active terrorist groups, Antonio - not his real name - is a philosophy student at the University of Rome. He is not particularly worried about graduating, however.

He insisted on anonymity because advocating terrorism is a crime in itself in Italy.

A native of a small city about 60 miles from Rome. Antonio stays enrolled at the university to avoid the draft. His main interest is politics, his major desire is for revolution, and his principal conviction - even though he is not ready to go underground himself - is that armed political violence and terrorism are the best way to make his revolutionary dream come true.

"Violence is necessary because the bosses and the fascists who run the state use violence against the workers, inside the factory and out," Antonio says. "Agreements between the union and the government that are worked out over the heads of the workers are violent, the police are violent and an economy that favors capital over labor is violent. We must fight fire with fire."

A recent survey of Italians between the ages of 13 and 23 shows that only a minority approve the use of political violence. Antonio, therefore, is not typical.

The same survey shows, however, that 28 per cent of those interviewed "could understand" the behavior of youths like Antonio who have rejected traditional politics.

In an analysis of violence of leftist terrorists, police records show taht of the 150 "actions" carried out by the Red Brigades since their appearance in 1970, almost 130 have been directed against major Italian factories or their personnel. Another group, Armed Proleterian Nuclei (NAP), has focused on Italian prisons where it recruits followers among ordinary criminals. In 1975 it kidnaped and interrogated a judge known for his expertise in prison reform.

While police estimate that active leftist terrorists probably number no more than 500, Alessandro Silj, whose book on terrorists, "Never Again Without Arms," was published here last month, says that "they may have a couple of thousand supporters scattered throughout Italy who give nonviolent assistance when necessary."

Police records show that last year alone there were 1>353 deliberate "terroristic" episodes and that unplanned outbursts of political violence now occur at the rate of about 20 a day.

Sociologists say the figures reflect a growing tolerance for violence in a society where political ideas were formerly expressed mainly through words.

After years of bombings and plots by authoritarian-minded rightist organizations, however, there is general agreement that most of the recent terrorism appears to be the work of leftist, self-defined policies now followed by Italy's powerful Communist Party.

"The Communists are an authoritarian Social Democratic party that has sold out the revolution in favor of economic recovery capitalist efficiency, and membership in the establishment," says Antonio.

He and his friends believe that Italy's unstable economic and political situation have created "pre-evolutionary" conditions here. They consider Italy 'an imperialist state dominated by the multinationals" that rides roughshod over the workers' interests and, because of the intrinsic defects of capitalism, is nearing collapse.

"The real party of the left is thus made up of terrorist groups whose actions are designed to demonstrate the state's weakness, sharpen class consciousness among the workers, and stimulate the unification of revolutionary gorups into a single armed party," says Antonio.

Offshoots of the extremist but nonviolent political groups that grew out of the Italian student movement of 1958, Italy's leftist extremists have increasingly turned to violence.

In recent years persons claiming membership in the Red Brigades, the NAP and three newer groups - "Front Line," "Communist Fighting Units," and 'Armed Struggle for Communism" - have been involved in a series of deliberate attacks on Italians from almost all walks of political and professional life. Most have been shot in the legs.

They are also thought responsible for a growing number of bombings, car burnings, factory fires and an occasional murder thought likely to speed up a general Italian crisis.

"The idea," says Antonio, "is to push the Communists and the Christian Democrats into an alliance that will disregard the workers' interests and radicalize them as well by the institution of new, repressive measures. Shootings and bombings serve to create a sense of panic and disaffection. People will realize the state can't protect them and will start to ask themselves why they should bother defending the state."

The extremists are described by insiders as fanatics imbued with revolutionary mystiques. In addition to Marx and Lenin, they have been influenced by the anarcho-syndicalist writer Georges Sores, the revolutionary writer Frantz Fanon, the Black Panthers and George Jackson and the Soledad brothers. Both the Red Brigades and the NAP are organized well enough to have hideouts and weapons caches in many Italian cities.

They appear to be largely self-financed by the proceeds from robberies, and from kidnapings police say so far have netted each group at least a million dollars.

While escalating terrorism has created widespread concern about Italy's future stability, government officials have said recently they believe the situation will be brought under control.

They say the terrorists will be defeated because they are misreading the Italian situation and because of their aims and methods have been rejected by all of Italy's traditional parties. In addition, a new government program worked out by Italy's six major parties, including the Communists, includes provisions for extended police powers.

Antonio, however, does not agree. He says that in the future the terrorists will be able to draw on the support of an increasingly radicalized youth.

"You see," he said, "many young people, both workers and students, are so turned off by widespread social injustice and by our politicians' wheeling and dealing that they don't feel they have much of a stake in Italian society as it is today."