Was Shakespeare actually the author of his plays?
The overwhelming scholarly consensus is yes — and the authorship question persists not because the evidence is thin but because the evidence is of a kind that disappoints people who expect a genius to leave a paper trail.
What the documentary record actually contains:
Contemporary attribution. Plays were published under his name during his lifetime, and other writers referred to him as their author. Ben Jonson, who knew him personally, wrote the dedicatory poem to the First Folio of 1623, compiled by two of his fellow actors — colleagues who would have known perfectly well who wrote the material they performed.
Theatrical records placing him as an actor, a shareholder in the company, and part-owner of the Globe.
Mockery by a rival, Robert Greene, in 1592, complaining about an upstart actor presuming to write — an odd thing to invent about a front man.
His will, which leaves bequests to fellow actors.
Why doubts arose. Not until the mid-nineteenth century, some 250 years after his death, did anyone propose otherwise. The recurring objection is social: a glover's son from a provincial town with a grammar-school education seems an unlikely author of courtly plays. But an Elizabethan grammar school taught rigorous Latin rhetoric, his sources were largely available in print and translation, and his plays contain geographical and courtly errors an insider would have been less likely to make.
The alternative candidates — Edward de Vere, Francis Bacon, Christopher Marlowe and others — each face decisive problems. De Vere died in 1604, before several plays were written. Marlowe died in 1593. Bacon's prose style resembles Shakespeare's not at all. Stylometric analysis consistently groups the plays with each other and separates them from the candidates' known work.
What is genuinely debated is far more interesting: collaboration. Early modern playwriting was frequently a shared trade, and modern scholarship attributes parts of several plays to co-authors including Fletcher, Middleton and Marlowe.