What kind of weird words is it that you use in the Academic Art of Riding? Here you get a short explanation of different words and concepts used in the Academic Art of Riding.

Aids – The signals you use to communicate with the horse.The primary aid is the seat. You can never remove your seat and it will always affect the horse, whether you want to or not. The secondary aids are reins, legs, whip, spurs and voice. These you can refrain from using.
– The first neck vertebrae.
Axis – The second neck vertebrae.

Bended stragiht – The horse has an even bending and chest rotation but moves on a straight track, ie it is not crossing its legs. It can be straight along the wall or on a circle. Imagine the horse’s legs moving on a railway track. The outer legs have one track and the inner legs have another track. The two tracks are parallel and never cross each other in bended straight.
Bending – The horse is bent like a banana through its body, from the neck to the tail.

Cavesson – A bitless bridle. You have either a solid or a bendable piece of metal around the nose of the horse. Has the same function as a snaffle, ie you can use it for stelling. 
rotation – With correct bending the inner hip will lower when moving forward and the the spine is rotating slightly, which creates a slightly higher outside and a slightly lower inside.
Collection – The horse angles its hind legs and carry more weight on them.
Curb  – A straight bit with with shanks for lever action. Its effect is to make the horse search forward down. Cannot be used for stelling, but this must be done by the seat or with a snaffle/cavesson.

Direct rein – Taken in the mouth, for example for stelling.

Ground work – Work from the ground. You walk backwards and is placed quite close in front of the horse’s head.

Indirect rein – Is added on the shoulders and move the shoulders in or out.

Longe – Longe line or longeing. ”Use the longe to slow down the horse” = use the longe line to slow down the horse.
Longeing – The horse is moving on a circle around you and you hold on to it with a long line.

Pirouette – The horse steps on one place with its hind legs while striding around the hind legs with its front legs. Demands quite some collection. In principle a very centered quarter in.

Renvers – Counter quarter in

Quarter in – The horse is bent through its body and the hind legs are moved inside of the track. The outer hind leg carry more weight.

Schooled halt – Work in the halt. In the halt you ask for shoulder in, quarter in, forward down and collection.
School halt – A very collected halt where the horse angles its hind legs very much and lift one front leg off the ground.
Shoulder  in – The horse is bent through the body and moves it shoulder slightly inside of the track. The inner hind leg carries more weight.
Snaffle  – One or two- jointed bit working by direct pressure. Used for stelling.
Stelling – A flexion of the neck, where the inner ear ends up lower than the outer ear. The mandible is bent in under the wing of the atlas vertebrae (the first neck vertebrae).

Travers – Quarter in

Versade – Shoulder in