What evidence do we have of the existence of an Indo-European language?

Answer 1

Proto Indo European is a hypothetical Mother language for the modern Indo European Languages. It is a linguistic reconstruction based on comparative studies of languages belonging to the Indo European language group.

PIE was developed initially in the 19th century by thinkers who initially were searching for the Adamic Language - that is, the language that Adam and his descendants would have spoken before the fall of the Tower of Babel and the confusion of the tongues in the Bible. Around this same time in history, there were many utopian language projects such as the creation of Esperanto and Volapuk, and the nation building projects of Western Europe that, in part, forced a national language onto citizens.

Proto Indo European is a useful tool to think about how languages are related historically, but is unlikely to have been an actual language.