Ballet is at once the oldest and the youngest of the arts. The impulse to dance must be at least as old as the impulse to sing; but the first professional ballet dancers appeared on the scene only about 300 years ago. It is also the only high art whose foundations were laid in recent times by amateurs, and by royal amateurs at that. The French court put on ballets the way some of our own ancestors may have put on amateur theatricals or played at charades, and the dancers were drawn from the members of the Court, including at least two French kings, Louis XIII and Louis XIV. Many of the gestures in ballet to-day still reflect the body language of the nobility of the seventeenth century.

Dance history can be approached in different ways. You can address the history of dance as an art, listing the great teachers and choreographers who influenced its development; or the history of performance, naming the stars and describing their careers; or the social history, discussing how theatrical dance interacted with the social and economic circumstances in which it found itself. The material that follows is largely the history of dance as an art.
Modern, or contemporary, dance is (naturally) a recent development. Where the history of ballet goes back four or more centuries--depending on when you date its origins--modern goes back only about a hundred years. Hence the entries here inevitably have much more to say about ballet than about modern.

Who invented ballet?

No one person did; it evolved gradually from the popular dances of the period. Many of the steps still bear names relating to the dances or the geographical regions from which they were drawn--for example, pas de bourrée and pas de Basque.  

I thought ballet was a Russian art.

Many of the greatest dancers in the 20th century have been Russian, but ballet arose in Italy and matured in France. In the 19th century, ballet flowered in Russia (through the work of French and Italian teachers who moved there), and early in the 20th century Russian ballet began to influence Western Europe, largely through the agency of the impresario Serge Diaghilev. Diaghilev's Ballets Russes gave ballet in Western Europe a much-needed shot in the arm, and the influence of Russian dancing, augmented by the various Russian companies who have toured Western Europe in recent years, persists to this day.

When was the first ballet?

That's open to debate, because there's no general agreement on how balletic a performance has to be to qualify as a ballet. Two performances are usually singled out by historians, however. One is a danced entertainment that was put on at a banquet celebrating the marriage of Gian Galeazzo, Duke of Milan, in 1489. Each course of the banquet was introduced by a dance. But the dances told stories, and so this is occasionally reckoned as "the first ballet." The other pioneering performance was the Balet Comique de la Royne (in modern French, Ballet Comique de la Reine), put on by Catherine de Medici in Paris in 1581 to celebrate yet another marriage. The libretto and choreography for this ballet are generally attributed to Balthasar de Beaujoyeulx. The dancers were members of the Court. The performance, which included singing and recitation as well as dancing, lasted more than five hours, and its expense was ruinous.

We know that other balletic entertainments were put on in between these two events, and it seems pretty clear that dance was presented as an artistic entertainment before 1489, but these are the events most frequently cited.
Ballet is generally considered a French art, but it should be clear that it has its roots in Italy. There was that performance in 1489; Catherine de Medici was Italian and may have brought the ballet with her; Beaujoyeulx was an Italian (originally named Belgiojoso); and the very word ballet is derived from the Italian balletto. But the first school was in France, the terminology is nearly all French, the most important early books on the subject were French, and it was the French who turned it from an entertainment into an art.

One of the earliest landmarks in ballet appeared shortly after the Balet Comique. The book, Orchésographie, written by a priest, Jehan Tabourot, under the pseudonym Thoinot Arbeau, appeared in 1588. In this book, there is no clear distinction between ballet and social dancing. Ballet evolved out of social dancing, and Arbeau's book gives us a snapshot of the era when this evolutionary process was still going on.

What is the oldest surviving ballet?

If by "surviving" you mean, continually in the repertory of a company in essentially its original form, the oldest ballet is apparently The Whims of Cupid and the Ballet Master, choreographed in 1786 by Vincenzo Galeotti for the Royal Danish Ballet. La Fille Mal Gardée is sometimes said to be the oldest, but it appeared three years later than Whims and the original choreography (by Jean Dauberval) is lost, while the Danes have preserved the choreography of Whims largely intact.

An earlier candidate could be Le Mariage de la Grosse Cathos, choreographed by Jean Favier in 1688, but this has survived only in notation and while it has been reconstructed in modern times, it does not appear to have been continually in any company's repertoire.

When was the first ballet school started?

The Académie Royale de la Danse was founded in 1661 by Louis XIV of France. (We are told that his sobriquet, le Roi Soleil, "the Sun King," stemmed from his performance as Apollo in Le Ballet de la Nuit, although Jacques Barzun claims that Louis XIII had the title before him.)

Whether the Académie was a ballet school as we think of them today is uncertain. The French use the term somewhat differently than in English-speaking countries, and an Académie is apt to be as much a standardizing organization as a school. (Think of the Académie Française.) The charter of the Académie Royale de la Danse suggests as much: it was to "reestablish the said art in its perfection, and to increase it as much as possible"

So it may have been as much a school for dance teachers as for dancers. In any case, it codified and standardized much of the teaching of ballet. (The five positions of the feet were either defined or standardized by the Académie.) Its most notable member was probably Pierre Beauchamps, who had been the king's personal dance instructor. This school was later merged with the Académie Royale de Musique, and was eventually absorbed fxinto the Paris Opéra.

From this background you can understand the roots of ballet: folk dancing, first refined by the court, and then turned into a theatrical display and an art. Each of these influences made its own contribution: the court added gracefulness and dignity, and the theater contributed professionalism and virtuosity.

How did ballet develop after the founding of that school?

The century after the founding of the Académie marked the rise of professionalism in ballet. Ballets like the Balet Comique de la Royne were danced by noblemen, but after the founding of the Académie, the nobility were gradually reduced to the status of spectators and patrons, and ballet was performed by trained, professional dancers.

Early ballet differed from what we see to-day in several ways. First, performance was "in the round": dancers performed on the floor of a hall, with the audience surrounding them and looking down at them. It was as if ballet were performed in a stadium. Ballet started using the proscenium stage some time in the mid-1700s, and this had a considerable influence on technique. Second, dancers did not have the great extensions we see now; the leg was rarely raised higher than 45 degrees off the floor. Third, dancers do not appear to have jumped very much: most dancing was at ground level, terre-à-terre. The change to greater extension and more steps of elevation may have resulted from the use of the proscenium stage, since both extension and jumps are visually more effective there. Finally, dancers wore heavy costumes--and masks. (Ballet tights weren't invented until about the time of the French Revolution.) Ballets in those days typically represented the deeds of classical gods and heroes, and the masks may have been thought appropriate for such roles. Dancers were still wearing masks in the latter part of the eighteenth century; Noverre complains about them in his Letters of 1760.

Beauchamps must have had a large body of experience to draw on. It would be interesting to know just when the organization of a ballet class took the form it has to-day, but it probably began to develop in that direction soon after the founding of the Académie and may have been Beauchamps's work. He is credited with naming the five positions of the feet, introducing more steps of elevation, and emphasizing turnout. The positions and turnout are mentioned in a book dating from around 1700. The degree of turnout was probably only moderate; the 90-degree turnout we recognize as the ideal to-day (i.e., with the feet in a straight line, pointing in opposite directions) was a gradual development.

The first important book after the founding of the Académie seems to have been Maître à Danser ("The Dancing Master"), by Pierre Rameau (1725). This book contains descriptions of pirouettes, beaten steps, and jetés, and it particularly emphasizes the arms. (The entire second half of the book is devoted to the use of the arms.)