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Volapük is a constructed international auxiliary language devised circa 1879 but not fully published until 1880 by Johann Martin Schleyer, a Roman Catholic priest in the Grand Duchy of Baden in Germany. Schleyer felt that God had told him in a dream to create an international language.
Comparison to Esperanto
If you think Esperanto is bad, then you will hate Volapük. Instead of using the extremely common AEIOU 5 vowel system, it uses the much rarer eight-vowel system of North Germanic/Uralic languages. It has contrast between a, ä, and e (English technically has more than five vowels, but their subtleties are assumed and not codified). Most of the words are derived from English, with some from German and French, but essentially all of these words are morphed to the point of unrecognizability. As an example of this horrible mutation, the name "Volapük" itself is composed of two words derived from English, can you see it? No? Exactly.[note 1] Also, the accent is always on the last syllable of each word, so the name of the language should be pronounced "volaPÜK".
Volapük has four grammatical cases (versus two in Esperanto), adjectives have agreement rules more complicated than in Esperanto, and verbs have complex conjugations.
In short, Volapük is basically a garbled and unharmonious mishmash of Germanic, Uralic and Altaic. Your mileage may vary, of course, but Esperanto is generally agreed to feel more aesthetic to the ear (and to the brain).
Volapük was highly popular after its creation. By the time Esperanto was published, Volapük began to decline in popularity. Although there used to be millions of Volapük speakers, today there are believed to be no more than 30 and the language is mainly kept alive through the internet. 
The Dutchman Arie de Jong briefly revised and revived Volapük after World War I, for example by reinstating /r/ as a valid phoneme. Schleyer apparently thought that the Chinese would have trouble pronouncing that sound, so he got rid of it, mangling words like "rain" into lömib (rein in the revised version).
Surprisingly, there is a Volapük edition of Wikipedia and even more surprising is that it has over 122,000 articles as of November 2018. Pretty huge for a dying language with an estimated no more than 30 speakers, huh? Well actually, this is because a Volapük fan used a bot to make thousands of articles usually focusing on geographical locations back in 2007. An editor proposed that the Volapük Wikipedia be closed from editing, but the proposal was declined. . Several other Wikipedia editions in obscure languages have faced similar problems.
The word "Volapük" in other languages
In many languages (including, amusingly, Esperanto itself), Volapük (or a variation of it) often means something like "gibberish". In Russian, "волапюк" (volapyuk) refers to a system invented for using early computers with Roman-alphabet keyboards to write a semblance of Cyrillic text. The word волапюк (or воляпюк) looks and sounds funny to Russian speakers, so it was a natural choice for naming such a cobbled-together system. (See the Wikipedia article on Volapuk encoding.)
- Answer sheet: "vola" derives from "world", and "pük" from "speak".