George Balanchine, one of the greatest choreographers in the history of ballet and the co-founder and artistic director of the New York City Ballet, died yesterday.

Mr. Balanchine, who was 79 years old, died at Roosevelt Hospital of pneumonia, a complication that arose from a progressive neurological disorder.

In guiding the New York City Ballet to international pre-eminence, Mr. Balanchine established one of the foremost artistic enterprises the United States has called its own. As a 20th-century master, his personal contribution loomed even larger.

More than anyone else, he elevated choreography in ballet to an independent art. The plotless ballet became a synonym for Balanchine ballet. In an age when ballet had been dependent on a synthesis of spectacle, storytelling, decor, mime, acting and music, and only partly on dancing, George Balanchine insisted that the dance element come first.

'See the Music'

In his dictum that the material of dance is dance itself, he taught dancers and the public to look at ballet in a new way. In his attraction to the very essence of dance - movement, steps and combinations of steps - he enlarged the ballet vocabulary as had no other 20th-century choreographer.

And because his choreography was so closely related to the music, a Balanchine work, in his words, became an invitation to ''see the music and hear the dancing.''

Like Stravinsky and Picasso, the 20th-century modern artists with whom he has been ranked, Mr. Balanchine was an innovator who came out of a classical tradition.

The hallmark of the Balanchine style was, indeed, its conscious use of tradition as a base. The idiom in which Mr. Balanchine chose to work was the 400-year-old academic movement vocabulary he had learned as a child in his native Russia at the Maryinsky Theater.

It was at this imperial theater in St. Petersburg that the 19thcentury French-Russian choreographer Marius Petipa created his greatest works, including ''The Sleeping Beauty.''

Because of his return to Petipa's classical idiom at a time when ballet borrowed from freer-style movement, and because of his own foremost role in the development of a 20th-century neo-Classical style, Mr. Balanchine was often called Petipa's heir. Willingly and ''very definitely,'' as he said, he was flattered by the attribution. He called Petipa his ''spiritual father.''

Yet as he made abundantly clear, the Petipa heritage was to be used as a springboard for expanding the ballet vocabulary and the capacities of dancers in 20th-century terms.

In every sense, George Balanchine was a modern artist. Balanchine dancers danced the same steps as Petipa's, but they were partnered at perilous angles undreamed of by Petipa and at a speed that could exist only in the 20th century.

Tradition was the base for renewal, and radical innovation could come only from those steeped in tradition. This belief was central to Mr. Balanchine's work, and it was reiterated in print by Lincoln Kirstein, the distinguished dance scholar who became Mr. Balanchine's patron and co-founder of the City Ballet and its precursor companies. More Than 200 Major Ballets

Together they established the School of American Ballet in 1934 and embarked on a venture that helped raise ballet to the highest status it has ever enjoyed in the performing arts.

It is very likely that Mr. Balanchine's genius - undisputed even by those opposed to his formalist esthetic - would have eventually flourished in any situation. But there is no doubt that Mr. Kirstein's invitation to Mr. Balanchine to come to the United States in 1933 made it easier.

The result was a creative output that raised the total of major Balanchine ballets to more than 200, only a few of them dating from the choreographer's years in Russia or in Serge Diaghilev's Ballets Russes and other European companies.

Throughout his career in the United States, the clarity of Mr. Balanchine's artistic vision remained remarkably consistent. The goal was a school and an American Classical company with its own new works rather than 19th-century classics and revivals. The museum concept was ruled out. Spectacle would be subordinate to dancing. Musical Collaboration a Priority

Distinguished musical collaboration - illustrated in Mr. Balanchine's association with Stravinsky - was a priority. ''Whether a ballet has a story or none, the controlling image for me comes from the music,'' was the way Mr. Balanchine explained his own work, and he then proved it in ballets that not only ''visualized'' the structures of their scores, but also contributed a dimension of their own to the music.

Above all, a Balanchine ballet, the work itself, was more important than the individual dancer. The result was Mr. Balanchine's celebrated no-star policy.

''As soon as you start selling a person, that's commercial,'' he once explained. A deeper reason lay in his insistence on the purity of movement, uncolored by the idiosyncrasies of a star performer.

Consistently, however, Mr. Balanchine used dancers of star quality who helped create the image of a new kind of dancer. The speed and sharp attack with which City Ballet dancers performed were singular. Ensemble Always the Star