The 12th sonata of Opus 1 is a set of variations on the ubiquitous 'La Follia' melody. The melody itself was derived from the original chord progression. Folia (Spanish for folly) first appeared in print sometime in the 17th century, but the original may be considerably older. Over three centuries many composers have used the tune and chord progression, from Jean-Baptiste Lully in the middle of the 17th century to Rachmaninoff in the 20th century have found inspiration in the minor key theme. The actual number of composers who have used it is ongoing. There is a website called La Folia A Musical Cathedral that is attempting to list uses and derivations of the theme with a list of composers that is quite long as well as a history and chronology.
Vivaldi composed the sonata for two violins and continuo. The recording that is linked below has a continuo section that includes cello, keyboard and theorbo. The theorbo is a long necked lute that made available more bass notes and was usually used as a continuo instrument.