Dressage

English dressage is a sport that involves a rider to have very good positioning while doing such things as walking, trotting, and cantering.  The riders are in a fenced in arena with little cones with letters on them outside of the ring.  The rider must do a various number of things in a certain order at different point in the ring As if that is not hard enough the pattern must be completely memorized by the rider.

Western dressage is basically the same as English dressage.  They both have to do flat work and have a memorized course.  The only difference is that some of the moves are different than in English, especially the halt.

Cross country is an event in which the rider has to go over many jumps in the shortest amount of time.  Riders must stay in the jumping position at all time even when they are not jumping.  The riders do not have to memorize the course and just have to do the jumps as they come to them.  

Show jumping is just like cross country except for a couple of differences.  In cross country you have no course to memorize but in show jumping you do.  In show jumping you only have to go into jumping position when you are going over the jump, not all of the time.  You also do not have to do the jumps as fast as you can.