After 25 years in the travel business, Arthur Frommer is so casual about flying off to the world's glamor spots he's been known to hop a trans-atlantic flight without so much as a toothbrush.

"I go somewhere -- to the Caribbean, to Mexico, to Hawaii -- almost every week of the year," says the bestselling author of Europe on $5 a Day , a classic in guidebooks that helped send America's jeans-and-backpack generation streaming overseas.

"I may leave the office at 4 and fly out to Madrid," says Frommer. "When I get there, I'll buy shaving gear and a spare T-shirt."

Hardly the way to cut costs, however, the whole idea behind Frommer's book, which over the years has kept pace with inflation by $5 title raises. The upcoming 1982 edition: Europe on $20 a Day .

But the good news, says the 51-year-old Yale University Law School graduate -- who gave up a legal practice when his travel empire flourished -- is that the resurgence of the dollar abroad is making Europe once more a "feasible" vacation destination for the less-affluent, from student to retired.

"I fought to make the title '$15 to $20 a Day,'" says Frommer, "but my publishers wouldn't let me. It' no longer a great deal of trouble to limit yourself to $20."

The travel industry, he says, is revving up for heavier translantic travel following the slack years since the mid-'70s when the dramatic rise in the price of oil sent airfare and other tour costs soaring. "Suddenly, Americans felt like paupers in Europe."

What amounts, he says, to "a 30 percent rise" in the value of the dollar in some countries "makes the most astounding difference. Suddenly everything is reasonable again."

For example, good theater tickets in London cost about 5 pounds. At the current exchange rate of about $1.85 to the pound, "that comes out to $10 (actually $9.25) as opposed to $16 to $17 six months ago." (This, he notes, is the price for orchestra seats. "In my book, I list gallery and balcony prices.")

At the Carvery, a popular London restaurant, a complete meal -- "a totally unlimited buffet table, smoked trout, dessert trolley, including service charge and tax" -- goes for about 6 pounds, 95 pence. "I don't have my calculator, but today that't around $11 (closer to $13)." But when the dollar was at its worst, "that same meal was $18 or $19."

But Frommer "wouldn't dream of recommending the Carvery" to budget travelers, even at today' prices, unless they're looking for a big splurge. Instead, he has found independently owned restaurants "with pretensions to high cuisine" all over London. He has dubbed them "Pots," as in "stewpots and stockpots. You can eat for 1 pound, 50 pence or 2 pounds.

"This new refreshing price level," he says, can be found all across Europe, especially the southern European countries of Greece, Portugal, Spain and parts of Italy. The continent again "has become the cheap destination."

At the same time, he says, airfares are leveling out. And, with no sudden fuel increases expected to upset pricing, there's a feeling charters will resurge.

Frommer's $20-a-day budget covers only the price of a room and three meals. "It obviously cannot include shopping and travel." That means, also, you must avoid first-class hotels and stay in small, sidestreet pensions, bed-and-breakfast establishments and second-and third-class hotels.

This is something, he has found, many Americans cannot bring themselves to do without making "a psychological adjustment." They are apprehensive, he says, about staying in a building without elevators or a private bath -- though they may work in a building where the bathroom is down the hall. But this alternative lodging -- "I recommend normal, clean hotels" -- can enable anybody in any city, he claims, to save up to 75 percent of their costs without giving up anything. (For the "starvation budget" traveler, he recommends youth hostels, college dorm rooms and other offbeat sanctuaries.)

The same type of accommodations, he says, exists in every city of the world, including South America and Asia. By sampling the lower-cost lodging, "You not only save money, you introduce yourself to a community of like-minded travelers. You meet other people with a drop of adventure in their blood."

The people who are constantly traveling, he says, often "have no greater resources than we do. The difference is, they are comfortable with budget travel. In London, bed and breakfast cost about 7 1/2 pounds per person, which leaves you with $7 for lunch and dinner."

Frommer is scheduled by Open University to talk Dec. 6 on shoestring travel and careers in the travel industry, a field, he says, which "is growing, and there are predictions it will be the largest industry in the United States.

"We are one of the most backward countries in the world in terms of vacation time -- most European countries get up to five or six weeks a year. This obviously has to change, even double. And when it does, the travel industry will double."

Frommer's empire includes a large tour operation and 41 other travel guides. But the annual edition of Europe -- which marks its 25th anniversary in January -- is a solo project. It all began back in the mid-'50s when he was stationed in Europe with the army.

"In my last two or three weeks there, I wrote a GI's Guide to Traveling in Europe ," an 80-page pamphlet based on his rambles through the continent.The Post Exchanges sold out in one afternoon. The next year, he updated it for civilians and has been on the road ever since: "I'd stumbled onto this voracious desire."

Though the constant travel may sound glamorous, Frommer calls it "slogging hard work," for which he may scout out a dozen or more out-of-the-way hotels and cafes in a day or two before moving on to the next city to repeat the search.

He admits that for business expediency, he often stays in the big hotels he urges budget travelers to shun. But on his own, he seeks out humbler establishments like the $14-a-night (double occupancy) hotel in Nice not far from the railway station (but blocks from the beach).

"You can come down to breakfast in your slippers, and get up from the table and go to the refrigerator if you need more butter."

His dream vacation?

Time off in West Hampton, Long Island. "Thats my idea of paradise -- not to travel."

Arthur Frommer's lecture, "Around the World on $15 a Day" is scheduled for Sunday, Dec. 6 from 10 a.m. to 1 p.m. at the Ramada Inn, Bethesda. "Careers in Travel" is offered the same day from 3 to 6 p.m. Question period. Each, $15. For more information: Open University, 966-9606 (Monday-Friday, 10 a.m.-5-p.m. )