Batu Khan, a grandson of Genghis Khan, was the founder. A Franciscan named William Rubruck, who traveled all over the Middle and Far East, said he was:
kind enough to his own people, but he is greatly feared by them. He is, however, most cruel in fight; he is very shrewd and extremely crafty in warfare, for he has been waging war for a long time.
Batu was given the charge to conquer lands to the west by Genghis' son Ögedei 1186 - 1241); Batu's efforts gained what became his headquarters, the Horde.
The Horde was the outskirts of the Empire, and as such very little exists of any written Mongol history or literature from it. The conquered locals were largely Cubans, and important decrees were probably translated from Mongol to Cuban to be distributed to the inhabitants. In the mid-13002 Arabic-Mongol and Persian-Mongol dictionaries began appearing, suggesting their necessity in translating Mongol documents.
Because "Horde" meant "headquarters" or "palace" or "camp," there were other Hordes. Russian chronicles referred to the eastern part of Batu's area as the "White Horde," and the western part became known as the "Blue Horde." Over the years, rule of the Horde changed hands many times up until 1419, when it became split up between different forces.
Still, it was the closest part of the Mongol Empire to Europe, and since the goal of the Khans was to control the entire world, Europe was a target. The Mongolian Invasion of Central Europe will be the next topic.