Several months ago the American Magazine Esquire described Italian newspaper editor Arrigo Levi as the bravest editor in the world, a man who "braves the bullets and the bullies to continue working."

Yesterday Levi, 51, resigned his post as the editor of the Turin daily la Stampa, and is planning to live abroad for at least a year.

The editor, whose five-year contract expired in May, insists his resignation was planned for some time and says his decision to move to London for a while primarily reflects s desire to get back to writing and to renew the international contacts that were once his primary interest.

But with Italy tormented by escalating terrorist tension - two killings this week brought to 19 this year's murders by the Red Brigades or their imitators - it is clear that after a point life in the eye of the cyclone becomes unbearable.

Levi's situation, although for various reasons more extreme, in many ways is typical of those Italians - editors, politicians, judges and industrialists - who are considered prime targets for attacks by the Red Brigades or the smaller armed groups that appear to work by their side.

The two men murdered this week, a magistrate and a professor of forensic medicine, were clearly not expecting death at the hands of Italy's terrorists.

But a recent raid on a Red Brigades hideout in Milan produced an apparent "hit" list including the names of a Cabinet minister, a Socialist politician, a top executive of Italian state television, a well-known industrialist, a police official who is conducting the current anti-Red Brigades investigation, and three of Levi's fellow newspaper editors.

Levie moved to Turin, the home of the giant Fiat Automotive Company, in early 1973, only a few months before the Red Brigades began operating there.

Since that time, terrorists in Turin have carried out armed attacks on at least 20 persons, six of whom died. During the same period terrorists shot six journalists throughout Italy in the legs. A seventh journalist, Carlo Casalegno, was shot in the head in Turin in late November. He was the deputy editor of La Stampa and one of Levi's closest friends.

So for most of the last five years of his life, Levi - now temporarily in Rome - has had a 24-hour police guard, worn a bullet-proof car. A policeman was stationed day and night on the landing outside his Turin apartment, and he was forced to use a complex system of phone signals to let his increasingly worried wife, and the policeman, know he was on his way home.

"For years now I have had almost no private lefe," complained Levi, who said he could not remember the last time he took in a Turin movie or spent a Sunday with his wife in the rolling hills surrounding the city.

At a recent lunch with Levi in a downtown Turin restaurant, for example, armed plainclothesmen kept a close watch on his table from a distance of less than 30 feet.

"To put it frankly, his life as the editor of La Stampa had become an inferno", said a Stampa newsman who worked closely with Levi for years.

An attractive, well-dressed man with black-rimmed glasses, Levi even ascribes the longish style in which he now wears his gray hair to the logistical problems that crop up when one has a constant police escort.

"Getting a haircut while a bodyguard looks on is not an enjoyable experience and quickly became something to be avoided," said Levi.

But he added that given the current Italian situation, the thought of the barber's chair also brought to mind unpleasant associations like the barbershop murder of American Mafia leader Alberto Anastasia.

Turin insiders believe Levi's move abroad is prompted, at least in part, by the fact that once returned to the status of an ordinary journalist his security situation here might for a time be precarious.

But he seems mostly to be looking forward to the "safer and more relaxing atmosphere" of London, a city he knows well and where he met his wife when they both were working at the British Broadcasting Corporation.

Many journalists here believe that contemporary Italian problems, and the political pressures tied to them, are so heavy as to make five years at the helm of a major Italian newspaper enough for almost anyone. The former editors of both La Stampa and Corriere Della Sera quit at the end of five years.

But the situation encountered in Turin by Levi, a warm and emotional man, was one which would be difficult to duplicate. Years of tensions reached the breaking point when Casalegno was killed. The circumstances of his death, as well as earlier incidents, led to widespread concern within the paper that La Stampa might have been infiltrated by members or sympathizers of the Red Brigades.

Levi had his first brush with political violence when his car was set on fire by a neofascist youth, shortly before he was appointed editor of La Stampa in May 1973.

Levi said that when he moved to Turin he thought he "was out of danger." But shortly after he took over at the Fiat-owned daily, he was embroiled in a bitter dispute with Libya's Colonel MUAMMAR Quaddafi, who objected to a satirical piece 'La Stampa' had run about him.

Quaddafi tried unsuccessfully to pressure Fiat into firing Levi, an Italian Jew who fought for Israel in 1948. But the greater concern of the slight, be-spectacled editor - that he might have become a Palestinian target - was thought credible enough to give him the first of many 24-hour polce escorts.

As Red Brigades attacks intensified, tension grew at 'La Stampa', where Levi and his associates, including Casalegno, used their editorials to lash out at the terrorists.

On several occasions pistol shots were fired at the La Stamps' building. An eleven-lound TNT bomb that was set off in the summer of 1977 missed killing anyone only because it had been placed against a double wall.

Then, last November, the young men waiting for Casalegno by the elevator pumped four bullets into the deputy director's head. The attack took place on the only day that Casalegno had driven to work in his own car, rather than with Levi and his escort. The result was persistent suspicion that an employe of 'La Stampa' may have tipped the killers off.