There is the story about the alligator who got to heaven and was asked to give his last wish. "Please let me have a shirt with a Giorgio Armani on it," he said.

A lot of people want to wear Giorgio Armani's clothes. Many already do: Jacqueline Onassis, Warren Beatty, Mick Jagger, Lauren Bacall, Richard Pryor, Candice Bergen. John Travolta became an Armani aficionado when he was fitted with Armani-designed costumes for "American Gigolo." Travolta dropped the film but insisted on buying the film wardrobe.

Giorgio Armani is the current "hot" designer, credited with singlehandedly making Milan a significant fashion center again, credited with starting the easy, unconstructed blazer for men and the oversized jacket for women even before Diane Keaton wore an Armani jacket when she picked up her Oscar for "Annie Hall."

At 45, looking like a Milanese Robert Redford, Armani spends most of his time with his coterie of workers, who are also his best friends. He rarely makes public appearances. Always tanned (it "helps the aging, my dear"), he has a soccer player's build, but is not at all athletic. Armani remembers buying a jogging suit and putting it on to run once around the block. It hasn't been out of his closet since.

Comfort is the ground rule for his own dress, which is usually a pullover sweater or knit shirt and pleated trousers. He sometimes wears a tiny eagle applique he calls the "Armani eagle." It's a symbol of freedom and a military decoration that, he says, is the only kind of decoration a man should wear.

Despite his $40 million-a-year worldwide business, Armani seems to be a soft touch. Once, when a Madison Avenue boutique owner was slow to pay the bills, he said, "Don't push her. She is so chic in her fox coat."

And when Travolta wanted the "American Gigolo" costumes for his personal use he was offered a big discount. "He liked my clothes so much and looked so well in them" Armani explained.

Armani says he is influenced by everything around him, everything he sees and does. The movies, the television, the art books. "I wish it weren't so. But I can't help being influenced by everything everyone wears," he says.

He takes no credit for the fact that Milan women ar so well dressed. "When you grow up in Italy it is hard not to be influenced by good design.All around you are good designs in buildings, art, furniture and the rest," he says.

And at the last Venice Film Festival he saw a film about a mime called Rataa-Plan. There was nothing remarkable about the clothes in the film. But the music! He asked composer Detto Mariano to extend the theme so he could use it as background music for his last show.(Total cost of that show -- $100,000.)

Armani watches over every detail in a fashion show, in the shop where his things are presented. He misses nothing. "In the corner of a fabulouss window display he can surely find one spot of dust," says Gabrielle Forte, who works for him in New York.

He works with the devotion of a country doctor, not an unlikely comparison because that is what he first studied to be. His bourgeois family at Piacenza in northern Italy had it all worked out. His brother was to study the classics and be a lawyer. Giorgio a doctor. "One studied piano, the other violin," he recalled.

When Armani found it difficult to concentrate and dropped out of medical school, the family didn't push. "They were intelligent and modern to that point," he says.

He has to stretch to find an early fashion connection. His grandfather did costumes for a small local theater and often talked about the productons at dinner. But young Giorgio never got to see any.

His mother had "classical taste" and like other Italian women in that surrounding, had one dressmaker to make her clother. But she relied on son Giorgio to help with the decoration of the house. And trusted his opinion on her clothes too.

After a brief try at photography, in the mid 1960's, Armani went to work for La Rinascente, a huge Woodies-like department store in Milan, then in its boom period. First he was an assistant menswear buyer, then fashion coordinator.

It was hardly a great period for men's clothing off-the-rack. Men who had money went to tailors. Those who didn't were offered an assortment of indistinguishable suits, always baggy enough to fit three sizes, and camouflage all individuality. Armani thought it was scandalous.

He was given the chance to learn something about menswear manufacturing and hopefully make some changes working as assistant designer in the Cerrutti company. They trusted Armani not to do anything outrageous. iHe didn't and many of his ideas were incorporated into the products.

But when Cerrutti started to make women's clothes in Paris, and wouldn't let Armani try his hand at designing them he quit. He was sure that many of the ideas he has applied to manswear would work for women.

With his good friend Sergio Galeotti, still today his "50-50 partner," as Armani describes it, they went into business. It took no investment of money since neither had any. In fact, when they needed money, without telling Armani, Galeotti would go back to his former job as menswear buyer at Larus, a fine men's specialty store in Milan.

Soon Armani was free-lance, designing for some of the largest manufacturers in Italy, with some of the clothes exported to the United States. Never with his name in the label.

Four years ago they started the Armani label, first the unstructured blazers, skinny lapels, longer proportions, which he showed to buyers in a first-floor apartment in the building where they lived. It started with menswear, with just a few items shown for women. But soon women wanted to wear his kind of easy, dressed but not over-dressed clothes and so he started separate women's collections with the impact in silhouette, fabric and color as strong as with the men's things.

From the start his designs were "knocked-off" quickly, blatantly, even before he had a chance to sell them. Armani once stood next to a man in a suit that copied precisely the draping of the jacket he had made for women. The man had tried to find the jacket in a man's department . . . no luck. Tried to find one large enough in a women's department . . . no luck. Finally he sent the jacket to a tailor in Hong Kong to copy in his style. Armani laughs and says through an interpreter, "I only wish they wouldn't copy me quite so fast."

Looking back at last fall's collection, which provided the draped jacket, he can find flaws. The skirt is too tight, women must keep tugging at them.And the draped waistline jacket . . . it was an effort to make something very feminine after a military or boy scout-influenced collection. It is too indentifiable of being of one season, he says. And along the way it lost the modernity of clothes that are comfortable, he says.

He has no such problems with is courrent spring collection. "It's my best," he says freely. "It it is the one where I was influenced only by what I thought was right. If there was insecurity at other times, in this collection there is nothing against my better judgment."

And there is no question, the lean jackets, sometimes collarless, sometimes with one lapel, the blouse with the off-side ruffle, and the suits teamed sometimes with easy cut pants and even shorts, and the soft evening things have been his best yet.

Even the strapless jacket which he admits started as a joke, he now feels strongly about. "Even in Milan, where people are conservative, women like strapless things when it is hot," he says. And to underscore the point he has done his jacket with a single lapel, a breast pocket and a pocket hankie, only minus sholders and sleeves. There is even a version as a bathing suit.

Besides, he says, the shoulder is one of the prettiest parts of a woman's body.

When the collection was finished in October he immediately started working on the next. First picking the fabrics . . .(next season they will be all exclusive designs), then matching the fabrics to his sketches. Next the canvas (toile) is made and once approved, enough fabric ordered for the first sample. Before he took a short holiday in December he was already fitting the first garments on a model.

For vacation or work he is rarely without some of his business family. Sergio Galleotti, his partner, has the final word on all business matters. Marisa Bulleghin gets the official title of "assistant" and does much of the technical work for scouting the fabrics to handling details on fashion shows. She's around full time to bounce ideas from him.

Gini Alhadeff, a niece of Aldo Pinto who heads up the fashion house of Krizia in Milan, describes her role as . . . "resident clown, getter of aspirin . . . the official weirdo, a provider of encouragement and a traveling companion." Alhadeff, who was born in Egypt and left a job at the Museum of Modern Art to work for Armani, is also his official translator. He can converse in French but he barely speaks English. (She told him the joke about the alligator.)

They seldom are away from him, always encouraging, testing ideas, feeding fresh thoughts, offering opinions. Armani trusts them, listens carefully and respects their views. They are his business friends and his vacation friends. They start the day with him when he unlocks the doors of his business compound in a Renaissance palazzo in the Via Ourini, and leave with him when he closes up 15 hours later.

Just as faithful is his bulldog, Gigi, although Gigi has asthma, is constantly huffing and puffing and dribbling on everything and a furry Persian cat, that always looks cross.

To relax, he says, he just does "silly things," busy work around his apartment (which is five minutes away from the office) or at one of his two vacation houses, one on the west coast of Italy, the other on an island between Sicily and Tunisia. His "family," dog and cat are there, too.

This week he will present his first menswear collecton made especially for American men. Last year, when he decided it was time to switch back to wide lapels in his regular menswear collectiom, the American buyers cried "foul." They were only just getting their customers in narrow lapels and felt it was too soon to change.

"American men are slower to accept new things," explains Alhadeff. So now there will still be the couture line for the very progressive things, and a special line for the Americans. Saks Fifth Avenue, Neiman-Marcus, Garfinckels, The Designers are among the Washington stores who will carry them. The range includes suits, shirts, evening garb, sportswear and raincoats.

For himself, on this trip to New York, Armani is sure to stop off at Bloomingdale's to make a purchase for himself -- white cotton boxer shorts with notched sides, he admits with a smile. But this is the last time. sHe'll start making them soon in his own workrooms.

On the last trip to New York in November he was approached for his autograph on Fifth Avenue. "So you se," he boasted to his colleagues in the office. "Now I am a star."

Armani is apparently one of the last to find out.