A few years ago, I arrived in Belgrade late one afternoon to discover the opera house across the street was performing Verdi's majestic opera "Aida" that night.

Did I know the company? No.

Did I recognize the names of any of the performers? No.

Was the conductor a reigning genius? Perhaps, but I'll never know. The billboard and the program were both in Serbo-Croatian. "Aida," "Verdi" and that day's date were the only words I comprehended.

Though Verdi's music is very familiar, it is presented only rarely these days -- too expensive is one excuse -- and I was very much aware of how infrequently an opera fan like myself happens to be in the same city where there is a performance. I snapped up a ticket at the back of the house and reveled at my good fortune.

The settings and costumes were lavish -- surely funded by a Yugoslavian government subsidy -- and the conducting and singing thoroughly professional. Only one thing was disconcerting. The singers sang in an unfamiliar tongue -- I took it for Serbo-Croatian, too -- so I heard a lot of clipped gutturals in phrases where my ear had become accustomed by recordings to gliding, romantic Italian. It wasn't quite the same "Aida."

My experience was a reminder of how abundantly available the performing arts are in Europe. Visitors in search of opera, ballet and symphonic classics can treat themselves almost nightly to performances by many of the world's leading companies -- and by many other less well-known but still excellent groups as the one in Belgrade. The principal season for music and dance is from now through spring.

The arts calendars in Europe's capital cities and in its smaller towns are filled with music and dance. If a full diet of opera or orchestral concerts is too expensive for your budget, you might vary it with a luncheon chamber concert -- they are popular in London and elsewhere -- or an organ recital in one of the Old World's ancient cathedrals.

We get a bit spoiled in Washington, where many of Europe's major orchestras visit on tour. But there is something special about hearing a superb company such as the Concertgebouw Orchestra of Amsterdam in its historic home on the Museumplein. The 2,200-seat Concertgebouw, literally "Concert Building," is regarded as having near perfect acoustics.

When you attend a concert in a foreign country, the experience is much more than simply hearing and enjoying great music. It is fun to watch the concert-going habits of the locals and to see them dressed in sometimes quite elegant fashions. And the concert hall itself often is an attraction.

The interior of the Concertgebouw, for example, is something of a theater-in-the-round, where the orchestra sits in the center almost completely surrounded by the audience. We took seats above and behind the players, which meant we looked down over their shoulders toward the conductor. During the concert, we could watch the conductor's face, just as the players did, rather than his back.

The Vienna State Opera is housed in another wonderful structure, so ornately decorated I began to think the rest of the audience surely must carry aristocratic titles. The Viennese tend to dress much more formally than music lovers in Amsterdam, and their fashionable attire can be part of the evening's entertainment. But don't plan on parading your mink down the aisle. Ushers will quickly -- and rather brusquely -- send you and anyone else with a coat to the checkroom.

There are no hard rules for getting tickets for performances. A travel agent can direct you to tour organizers who specialize in music and opera tours. One of the leaders is Dailey-Thorp of New York (1-212-307-1555). Its groups travel first class, so the tours generally are expensive. However, travelers can make ticket reservations directly with the concert hall, use a U.S.-based ticket agency (for some concert halls), a ticket agency in the city of performance or take a chance on finding seats when you show up.

If there is an orchestra, a work or an artist you particularly want to hear, it probably is wise to get reservations. We wanted to hear Mozart's "The Magic Flute" at the Vienna State Opera, so we sent in our money -- about $45 per person for orchestra seats -- weeks in advance. This proved wise since all the performances were sold out during our stay in Vienna. But on two other nights that week we bought day-of-performance tickets for balcony seats at a third of the price.

As a rule, symphony and chamber concert tickets are more easily obtained on the spot since performances are frequent. Tickets for ballet and opera, particularly for popular works, sell out more quickly.

Finding out in advance what is being played when is not always easy. Most standard guidebooks focus on the arts in the summer, which is the heavy tourist season, and ignore the winter months. Each Western European country has a tourism office in New York City, but these offices generally have a schedule of upcoming performances for only about a month in advance. They can give you the addresses of specific performing arts groups if you choose to contact them directly.

As sources of entertainment abroad, music and ballet have a distinct advantage over theater (except in Britain) and over movies that have been dubbed. You can enjoy them, as I did "Aida," in any language anywhere you are traveling.

If you are planning a grand tour of Europe's performing arts this season, or want only to sample one or two of its best companies, consider the following inviting destinations. They are only a sample of the wealth of music and dance offered.

London For the title of arts capital of the Western world, London is rivaled only by New York City, and it has the advantage for the ticket-buyer of generally lower prices. A fan of good music and dance could settle in quite comfortably for a long stay.

The city has not one, but several major orchestras -- among them, the Royal Philharmonic, the Philharmonia Orchestra of London, the London Philharmonic, the London Symphony Orchestra, the BBC Symphony Orchestra and the Academy of St. Martin-in-the-Fields. Conductors and soloists are among the most honored names in the music world.

On any given night, you are apt to find at least one of these orchestras performing at Britain's leading arts center, the South Bank Arts Complex, either in the 3,000-seat Royal Festival Hall or the smaller Queen Elizabeth Hall. A second arts complex, the new Barbican Centre, is home to the London Symphony Orchestra.

London's third musical complex is the Royal Opera House, Covent Garden, site both for performances of the renowned Royal Opera and of the Royal Ballet. A second opera company, the English National Opera, is housed in the posh Coliseum, an Edwardian delight of marble, mahogany and bronze. Its programs this season, all of them in English, include "Der Rosenkavalier" and "Hansel and Gretel."

London's other major ballet companies are the London Festival Ballet, appearing at the Royal Festival Hall and the Sadler's Wells Royal Ballet at the Sadler's Wells Theatre.

West Berlin Under the leadership of Herbert von Karajan, the Berlin Philharmonic Orchestra has maintained its place as one of the world's great orchestras. The big yellow-tinted, tent-shaped Philharmonie, its home, is designed so that the orchestra sits surrounded by the audience.

Tickets for a von Karajan concert sell quickly, and it is advisable to reserve in advance. Actually, you are more likely to hear the orchestra than view its conductor on the podium, because he is frequently on tour as a visiting conductor elsewhere.

In 1987, Amsterdam was dubbed the "cultural capital of Europe" by the European Common Market. The title meant that throughout the year, the rest of Europe sent many of their outstanding performing arts groups to that city. In 1988, West Berlin is Europe's cultural capital, and an extensive arts program gets underway in February.

Amsterdam Though Amsterdam is giving up its cultural crown at the end of the month, the performing arts calendar for the new year seems little diminished. While the Concertgebouw Orchestra under Bernard Haitink is the city's most famous performing arts attraction -- it celebrates its 100th anniversary in 1988 -- other options include programs of the Netherlands National Ballet and National Opera in the Stadsschouwburg, or Municipal Theater, on the Leidseplein.

The opera company doesn't rank among Europe's best, but the theater is small, and its intimacy adds much to your enjoyment -- that and the low price for tickets compared with what you pay to attend an opera in the United States.

Copenhagen The new year marks the 400th anniversary of the coronation of King Christian IV of Denmark, who was a patron of the arts and culture. The anniversary will be celebrated throughout the 1988 with many special arts programs.

But in any year, it is Copenhagen's Royal Danish Ballet that is the city's finest cultural attraction. With a two-century-old heritage, the company is steeped in the old classics, including many works of the famed 19th-century Danish choreographer August Bournonville. But the Danes are tolerant of new ideas, and the ballet company capitalizes on this with many thoroughly modern and often experimental programs. The ballet shares the two stages of the Royal Theater with the Royal Danish Opera.

A special event at the theater on May 7 is the first annual Hans Christian Andersen Ballet Awards ceremony honoring the world's best ballet performances. Some 38 ballet companies from 22 countries are expected to nominate candidates for four awards: best female performance, best male performance, best choreography and an honorary award of merit to a patron. The winners receive a porcelain statuette of Andersen, many of whose fairy tales have been worked into ballets.

One U.S. tour organizer has put together a one-week trip to Copenhagen for the awards ceremony and the week-long festivities surrounding it. The all-inclusive price, including air fare from New York, is $4,000 per person. For information: Stark Production Associates, 311 North Desplaines St., Suite 608, Chicago, Ill. 60606, 1-312-648-1280.

Paris The performing arts of Paris have undergone a revival in recent years, and visitors can expect excellent and often innovative productions from the Paris Ope'ra and the Paris Ope'ra Ballet, now led by Rudolf Nureyev. The Orchestre de Paris, under conductor Daniel Barenboim, has greatly enhanced its reputation also.

Milan La Scala, Italy's most famous opera house, celebrates its 200th anniversary in 1988. Opera buffs can visit the theater's museum during intermissions. But travelers to Venice (Teatro la Fenice), Florence (Teatro Comunale), Rome (Teatro dell'Opera) and Naples (where Teatro San Carlo is celebrating its 250th anniversary this season) should find opportunities to attend at least one performance of Puccini or Verdi in their homeland.