THE MUPPETS? The Muppets are nothing! The Muppets are only the tip of the iceberg.

There is a whole wide world of puppetry -- and this week Washington is its capital.

For the first time in a half-century, the quadrennial World Puppetry Festival is being held in this country, today through June 16, drawing people from 45 nations.

The festival is spread all over town: at the Kennedy Center, the Corcoran, the Smithsonian, the Hirshhorn, the Renwick, the Freer, the Museum of African Art, Georgetown and George Mason universities.

There are marionettes, hand puppets, finger puppets, rod puppets, shadow puppets, Senor Wences mouth puppets, stop-motion figures for Puppetoons, jointed Javanese wayang manikins, bunraku puppets, kachina puppets.

There are skeleton puppets; life-size armored Crusader puppets by the Sicilian family Manteo that spill blood and intestines when speared; a fat woman singer puppet that turns into a ballon; the Grand Turk, who bursts into six smaller puppets.

There are harlequins, acrobat puppets, 25-foot-high puppets that need five people to work them, Gordon Craig's elegant experiments in puppets as high art, handicapped puppets, puppets that operate other puppets, a U.S. senator puppet with two faces. . . .

UNIMA, the international puppetry organization, which now has centers in 55 nations, had its last world congress in Moscow. Some 1,000 delegates came to the 1976 event, and organizers expect nearly twice that many here this week.

What is it about puppets that inspires this kind of pancultural zeal? Ask the leaders of UNIMA, and all they can say is that it is just a bunch of enthusiasts, performers and scholars who take heart in each other's company. That helps, but not much.

"The magic of puppets? I don't think about it much," says Burr Tillstrom of Kukla, Fran and Ollie."I suppose it's like the appeal of cartoons," he muses, as though considering it for the first time. He's only had Kukla for 44 years. "It's like any fantasy or fairy tale: It engages your imagination."

When he and Fran had their daily show, it was entirely ad-libbed. But for the special last Christmas they did write a script of sorts. They still finished up with some spontaneous dialogue.

"The characters take on a life of their own after a point. As John Steinbeck once told me, a character in a novel starts to write itself. Though you don't lose control."

In Chicago last week for the Emmy Awards, Tillstrom and Fran were standing around with some stuffy executive types, he with the Emmy under his arm. All of a sudden the statuette started to talk. It just happened.

Tillstrom will be here this week, and so will Jim Henson, Shari Lewis, Bil Baird and others. They'll open the gala at the Concert Hall today at 3 p.m. Among the puppets attending will be Kermit the Frog, Miss Piggy, Big Bird, the Kuklapolitans and Lambchop.

"It goes right back to the beginning," says Nancy Lohman Staub, executive director of the 2,500-member Puppeteers of America. "You have the shaman, who could imbue objects with spirit. You have masks.Voodoo dolls. Pantheism -- the idea that rocks and trees can have souls. It's as basic as that."

For some of us, she observed, the suspension of disbelief -- or, better, leap of faith -- required to feel actual emotion at the manipulations of a block of wood is just too much. But for others, it is perfectly natural. It's easier than relating to actors.

"It's instinctive," she says. "It's an ability we have as children, but it is; educated out of us. We lose it as we get more sophisticated."

This is why children get such a kick out of puppet shows. For example:

The first and second grades of Savoy Elementary School in Southeast Washington sat on the floor of the Corcoran last week while Bob Brown and John McAnistan made a lot of funny little people dance and jog and fly on a trapeze. As the swing swept back and forth, all 48 heads turned with it in unison. When Gus the Clown waved, 48 hands waved back. When Brown, at the end, asked what kind of animal his puppets were turning themselves into, 48 voices instantly shouted, "Caterpillar!"

"A puppeteer has opportunities of self-expression that are simply unlimited," Staub says. "An actor is limited by the body. But with puppets you can bare your soul."

Henryk Jurkowski, general secretary of UNIMA, is in town for the festival. A scholar of the theater, he has specialized in puppetry for years in his native Warsaw.

"In the 19th century the puppet theater was a theater of the poor," he says, "because puppets were cheap to make. But then it mostly imitated the human theater. It is only in the last few decades that people are discovering the esthetic value of puppets for their own sake."

He relates the rising interest in puppetry to the parallel rise of interest in folk art. "Today in Europe we are seeing all sorts of new things: The puppeteers and puppets become intermixed, interchangeable perhaps. It is a new theater genre."

(One is reminded of a Bread and Puppets number in which live actors are pulled about on strings like marionettes.)

Serious puppetry in the United States has been around for years: Martin Stevens doing Aristophanes; Tillstrom with the WPA is 1936 presenting a Gertrude Stein play written for puppets; landmark performances of The Passion, the story of Joan of Arc, and so on.

Artists who have produced work for puppets include Haydn, Schiller, De Falla and Lorca, not to mention Alec Calder and his famous miniature circus, exceedingly chic in the '20s and roasted at some length in a Thomas Wolfe novel.

Today in America, puppetry is so popular that some of its creatures have become folk heroes of a sort. The Muppets alone are seen every week by an estimated 235 million people around the world. And a new Frank Oz Muppet, Yoda, threatens to run away with the Star Wars sequel, "The Empire Strikes Back."

Some puppet artists are more serious than others, of course. The form is perfect for social satire. There are Nixon and Roosevelt puppets at the Corcoran's show of puppets as art, for instance.

Also at the Corcoran -- wooden celebrities! Charlie McCarthy! Howdy Doody! Little Bird! Fred Horse! Punch and Judy! Pinocchio -- the puppet who crossed over!

A superbly mounted exhibit of 230 puppets -- from 10th-century pre-Columbian finger puppets to the Bread and Puppet Theater's 14-foot Duke of Naples -- plus video strips and hourly live performances all week by Bob Brown Puppets -- will be the scene at the Corcoran.

Next Sunday noon Peter Schumann, the acclaimed leader of the sometimes angrily political Bread and Puppet Theater of Vermont, will lead a parade of 50 puppeteers, giant puppets, jazz bands and people on 12-foot stilts up the Mall from 14th Street to the Corcoran.

Schumann says, "Puppetry is a great old form of theater. There must be young people around who are dissatisfied with the limitations of theater, who avail themselves of the powerful means of this old art form, who start fresh and free and have a great idea to follow and who have nothing to do with the thin and silly cutesy-pie stuff that people call puppetry, and that is used to stupefy adults and kids alike. Good luck to all puppetry revolutionaries! Bye-bye and sleep well to all the commerical junk."

The Corcoran has adult workshops, Thursdays at 7 p.m., through Aug. 14 and family workshops all day June 21.

There is the "Ring of the Nibelungen" by the University of Connecticut -- one of several American universities giving an MA in puppetry -- June 9 and 10 at 7:30 at the Kennedy Center.

Also at the Center's Eisenhower Theater: the East Bohemian Puppet Theater DRAK of Czechoslovakia doing "Sleeping Beauty" June 11 and 12, and a puppet ballet danced to Stravinsky (Petrouchka was a puppet, after all) and Bartok by the Hungarian State Puppet Theater of Budapest June 13 and 14, all at 7:30 p.m.

Albrecht Roser of Stuttgart will perform June 15 at 8:30 at the Terrace Theater with his celebrated marionette Gustaf. At the same location will be the giant puppets of the Montreal Theatre Sans Fil June 9 and 10, the Puppet Theater Puk of Tokyo June 11 and 12. Brazil's puppet troupes June 13 and 14, all at 8:30, and the Swiss Puppeteers June 15 at 2 and 4.

Some of the other events this week here:

A Puppetry Fair June 9-13 at McDonough Gym, Georgetown University, featuring exhibits and demonstrations from everywhere and a sales area.

Special performances at Georgetown: the Dutch Figurentheater on June 10, 12, 13, and 14; Bread and Puppet's "Joan of Arc" June 14; cabaret performances June 15. For information, call Puppeteers of America, 265-6564.

At the Smithsonian's Museum of History and Technology, a summer exhibition entitled "Puppets, Muppets and Things on Strings" opens today, with 20 puppets starring Howdy Doody, Charlie McCarthy and Mortimer Snerd. And the Smithsonian will hold folk puppetry performances all day June 11-14 on the Mall and in Baird Auditorium. Belgian puppets will perform at the Renwick Gallery in French through June 14.

There is a two-day scholarly symposium on puppetry at the History and Technology Museum's Carmichael Auditorium June 13 and 14 with an international lineup of speakers touching such subjects as "Bamana and Bozo Puppets in the Seagou Region of Mali."

The American Film Institute Theater will present Danny Kaye in "Knock on Wood" and Leslie Caron in "Lili" tonight at 5 and Tuesday at 8:30. On June 14 at 3:30 the California-based Bob Baker marionettes may be seen on film.

Puppet exhibits also will be at the Freer, African Art Museum, Hirshhorn, Organization of American States, Natural History and History and Technology museums. The latter will show Disney's "Pinocchio," among other films.