You can go to youtube and search "hip hop dressage" (freestyle to music) and Prix St Georges.
The basic gaits are walk, trot and canter. (There is no gallop in dressage)
But there are much more complicated. There are two degrees in collection. One of them are collection and collection plus.
Trot: extended, collected, medium
Walk: extended, collected, medium and walk on long rein
Canter: extended, collected
Here are some advanced movements.
Passage, piroutte, half pass and much more.
There is also classical dressage but only lipazzaner stallions can master.Its called "airs above ground" Lipizzaner a born black and when they grow their coats will turn white which we call gray horses.
Here is a lipazzaner stallion performing a courbette.
These moves are not for performing in the times when there's war, it's for defence and attack for knights riding on horses.