Eventing, also known as combined training, began as a trial for the Military's Calvary. Eventing is divided up into three phases, Dressage, Cross Country and Show Jumping. This can further be divided up into One Day Eventing, and Three Day Eventing.

Day one, or the first event is Dressage. Dressage is a test of balance, obedience, suppleness, and the overall skill and rapport between horse and rider. During this phase horse and rider most complete a specific pattern. The pattern is divided up into many parts. Each part targets a certain aspect of the horse and rider, such as balance, suppleness, etc. These parts are scored by the judge(s) from 0 to 10, ten being the best mark possible. Riders can be eliminated if the exceed more than three errors on course, all four feet of the house leave the arena during the test, or if the horse resists for greater than 20 seconds time. For the first error on course rider will receive 2 penalty point, for the second error on course the rider will receive 4 penalty points. Points are totaled ( Positive points for the movements, and negative points for penalties.) and divided buy the total possible points. Therefore dressage scores are actually percentages.

Day two, or the second event, is the Cross Country, a test of stamina. In this the horse and rider must complete along course, of "natural" jumps. A certain optimum time is set and riders must complete the course with in the time limits. If the do not, the incur penalty points for ever second they are over. As well riders are eliminated if they exceed three refusals at a single obstacle, two total falls, or exciting the time limit by double the optimum time. Riders can also incur 20 penalty points for their first refusal, 40 penalty points for their second refusal (at the same obstacle), 65 penalty points for their first fall, 0.4 points for exceeding the optimum time, 0.4 for coming in too far under the optimum time limit (this is mainly in the lower levels to keep riders for pushing their horses too hard.). Riders also must leave the course if their horse falls and his shoulder touches the ground.

Day Three, or the third event, is Show Jumping. In this horse and riders must complete a course of jumps. Again there is an optimum time, and a penalty of 1 point per second if the rider exceeds the time limit. Riders will also receive faults for knocking down rails, or not clearing a water jump, refusal, and falls. Riders can be eliminated for more than three refusals on the course, more than two falls on the course, jumping the course in the wrong order (and not fixing it).

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Information based off the information on Wikipedia.
For more information check out Eventing at Wikipedia.