Apparently vermouth was invented in 1786 by Antonio Benedetto Carpano (1764, Turin - 1815, Turin). The brand Carpano still exists and it's marketed as a vermouth based on the old recipe: Carpano Antica Formula. It's well worth the investment. Carpano Antica Formula is a sweet red vermouth 'Italian style' and full of spice overtones, orange, vanilla ... It's great to drink on it's own, but also an important ingredient for the Manhattan (whiskey, sweet vermouth, and bitters) and the Negroni (gin, Campari, red vermouth). But I would start drinking Carpano Antica Formula as an apéritif.
Carpano Antica Formula is nowadays made by the Italian distiller Branca.