Which lost Shakespeare collaboration is based on Cardenio from Don Quixote?

The lost Shakespeare collaboration based on Cardenio from Don Quixote is The History of Cardenio. The play is generally attributed to William Shakespeare and John Fletcher, although the attribution remains debated.

The King’s Men reportedly performed the play in 1613, and a 1653 Stationers’ Register entry identified Shakespeare and Fletcher as its authors. The surviving evidence is indirect because the original script has never been found. Its presumed source is the Cardenio episode in Cervantes’s Don Quixote, in which the young Cardenio is driven mad after betrayal and wanders in the Sierra Morena.

The work is sometimes called simply Cardenio. Its connection with the later play Double Falsehood is also controversial: in 1727, Lewis Theobald claimed that his adaptation derived from a Shakespearean manuscript, but the authenticity and extent of that connection remain unsettled.

The Two Noble Kinsmen is another accepted Shakespeare–Fletcher collaboration, but it is not the lost play based on Cardenio. That distinction makes The History of Cardenio the canonical answer here.