FOR MANY PEOPLE, CLASSICAL MUSIC is an enigma, a vast world of high-sounding ideals and mystifying terminology. Because it is perceived as a bastion of snobbery and because it is complicated, classical music has a limited audience. As the works of many contemporary composers are inaccessible, and since orchestras incessantly perform the same repertoire, classical music has in recent decades stagnated into glorifying the past.

Fortunately, if the music composed today too often seems removed from anything most people can understand and appreciate, saying that the conventional repertoire has nothing to say to "modern man" is like saying Shakespeare has little to tell us about the human condition.

With classical music's snob appeal and the air of mystery that surrounds it, it is all too easy to get turned off by it, or to avoid cultivating a taste for it.

But you can learn about classical music. There's nothing very mysterious about it, or at least nothing more mysterious than great achievements in any type of art. You can decide for yourself, damn the "experts," which composers and pieces you like. Classical music won't bite.

Even after listening many times to works well-established in the classical canon, some will shrug and ask themselves what the fuss is all about. Such is life. But many people may find in the music of the classical "greats" something missing from other types of music.

That something is not necessarily profundity, though it might be. It might also be wit, or melancholy, or languor. Classical music is not, repeat, not all serious. Once you understand its language, or languages, it has a much wider range of expression than other types of music.

The name "classical" is itself misleading because it suggests that there is some type of unity to the pieces that come under the name. There really isn't, though there are certain traditions within classical music.

If you don't play an instrument, the only real way to go about learning about classical music is to go to concerts, listen to recordings, and secondarily, to read about it. Many people see classical music as an amorphous, uninviting mess because unlike many other types of music, it generally has no words to help you remember the melody. There is no substitute for listening, and listening intently.

IT WOULD BE RIDICULOUS TO TRY to summarize music history here, but it does seem appropriate to give a very general overview. For many people, classical music starts with J.S. Bach, who represents the apex of the baroque musical era.

Everything before Bach is often lumped under the vague title of early music, a flourishing subfield. Besides Bach, well-known baroque composers include Handel, Vivaldi and Telemann.

The end of the baroque era is generally demarcated at 1750 with the death of Bach, who is not to be confused with his many less talented progeny. After the baroque era is the classical period, the time of Mozart, Haydn and others who are said to form the first Viennese School.

Beethoven and Schubert and the last great classical composers and the first greats of the Romantic era. The Romantics include Schumann, Chopin, Liszt, Mendelssohn, Dvorak, Moussorgsky, Tchaikovsky and Rachmaninoff, many of whom were inspired more by small forms like songs or preludes than by symphonies and concertos, which pair a solo instrument and an orchestra. The classical and Romantic repertoire forms the backbone of the music played most often in concert halls.

Johannes Brahms deserves special mention as a Romantic who continued the symphonic tradition of Beethoven. Other Romantic symphonists include Bruckner and Mahler, who both wrote works of great beauty and very great length. Richard Strauss and Richard Wagner are other well-known composers of about the same time period.

After the Romantic era, itself complex and varied enough, there is really no name under which to group the various composers whose works have stayed in the active repertoire. In France, there were, as in painting, the impressionists, including Faure, Debussy, Ravel, Chausson and Franck.

In Vienna there arose a second Viennese School that included Arnold Schoenberg, whose earliest music is the most listenable, Anton Webern, and Alban Berg. Their music is often contorted and bizarre, with very strong dissonances.