In the course of this ‘Fachbereichsarbeit’ a better insight has been provided into the ample world of Western Riding.
Some of these chapters definitely required (delete "a") further consideration, if they did not go beyond the scope of this ‘Fachbereichsarbeit’.
Cowboys and Vaquero might have differed a lot from each other. However, this would not change the fact that both chose a life in total isolation as well as decided for a close companion, namely the horse, to go through thick and thin with. (uncomfortable phrasing, but correct; keep the "with")
Be it a riding style, which once engaged the rider’s attention as little as possible; (this is not a correct sentence and before a semi-colon it must be a complete sentence. Try again. I'm not sure what the subject of the sentence is supposed to be.) today exactly this Western Riding Style combines freedom and independence, radiating pure ease and precision. (nice sentence here though)
With this in mind I would like to especially emphasize the elements of the Indian nations. Not only did they lay the foundation for a non-violent way of schooling a horse, (comma not semi-colon) thanks to selective breeding they also contributed a lot to the development of the Western Stock Horses, carefully preserving their heritage until today.
Is "Fachbereichsarbeit" supposed to stay in German or are you looking for an English word for that? I would use the word "study" maybe. (Perhaps someone who has done school papers will know a better word. It means kind of a thesis, but not quite so deep. It's not a master's thesis, but a supportive or disputing analysis of a subject.)
All in all - without reading the whole text preceding this, it sounds good; The only real issue I see is the phrase I have marked in blue. I won't be able to look again tonight, but maybe someone else can if you post another version.
Good job. I wish my German was as good as your English!