Short answers, pulled from the story.
The Parnassus plays are three satiric comedies written between 1598 and 1602 for performance at St John's College, Cambridge University. The three plays are The Pilgrimage to Parnassus, The Return from Parnassus, and The Return from Parnassus: Or the Scourge of Simony. They were performed as part of the Christmas festivities by and for students.
The authorship of the Parnassus plays is unknown. John Day was proposed as a possible author by Bolton Corney in 1868, based on an inscription in a copy of the 1606 quarto reading "To my Lovinge Smallocke J: D:", but the suggestion has had little support. Some scholars believe the author may have included a self-portrait in the character Judicio.
Shakespeare is mentioned by name in the last two plays and his works are quoted at least 95 times across the trilogy. He is mostly satirized, particularly through the foolish character Gullio, who worships Shakespeare devotedly. A famous scene features Richard Burbage and Will Kemp, members of Shakespeare's company the Lord Chamberlain's Men, auditioning two hapless scholar-actors.
The trilogy follows two students, Philomusus and Studioso, from their allegorical journey through university study in the first play to their failed attempts to earn a living as graduates in the second and third plays. Along the way they work as a gravedigger, a farmhand, a tutor, and briefly as fraudulent doctors, before ending as shepherds in Kent.
Only the third play was published, in 1606, and the first two were considered lost for many years. In 1886, W. D. Macray, the librarian of the Bodleian Library at Oxford, discovered the manuscripts while researching the Thomas Hearne collection within the Richard Rawlinson collection. He edited and published all three plays together immediately after finding them.
A handwritten manuscript of The Return from Parnassus: Or the Scourge of Simony is housed at the Folger Shakespeare Library. The manuscript is a small quarto volume bound in parchment, and its handwriting dates it to the period of the play's original performances around 1601-1602.