The Académie du Spectacle Équestre is based in the Grande Écurie, the king's former stables facing the palace across the Place d'Armes. Under director Bartabas, it presents regular performances of classical equestrian art — haute école dressage combined with theatrical spectacle — that are unlike anything else you will see at Versailles.
The shows run in the main riding hall of the Grande Écurie, a high-ceilinged Baroque space designed by Jules Hardouin-Mansart in 1682 to house 600 horses. Bartabas's productions combine precise riding — piaffe, levade, capriole, the full vocabulary of academic horsemanship — with music, often performed live, and a stripped-down theatricality that manages to be both austere and spectacular.
Performances run most weekends and some weekdays; check the schedule and book in advance. There are also morning rehearsal sessions (reprises matinales) where you can watch the riders training, which are cheaper and have a different, more intimate quality. Even if horses are not your particular interest, seeing this in a 17th-century riding hall with the palace just outside is a distinctive experience.