Edward de Vere (1550-1604) composed, and may have directed and acted in plays during his life. He managed a troupe called the ‘Oxford Boys’ and was embedded in the theatre community. He would also have had access to court and the necessary education to write at length on the subjects present in Shakespeare’s plays.
His status as a nobleman in Elizabethan England would have meant that he could not be seen putting his name to written works. It was not deemed appropriate for aristocrats to write, especially plays, as it was their role to serve the crown and not seek their own fame. Fame was for the monarch. They could manage troupes and finance performances, but writing plays was not considered a worthy pursuit of the nation’s noble stock.
His writing style closely resembles Shakespeare’s. The pair are the only two Elizabethan poets to use a six-line pentameter stanza. 
De Vere’s nickname was also “Spear Shaker”. It stemmed from his athletic prowess in tournaments and his coat of arms, which featured a lion brandishing a spear. He also lived near Shakespeare on the banks of the River Avon in Bilton Hall. Therefore, he would have been familiar with the Warwickshire area and the local landmarks that litter Shakespeare’s plays. Taming of the Shrew makes fun of a commoner in Warwickshire who finds himself drunk and dressed up like a nobleman.
The chronology also lines up. De Vere published several extant poems under his own name. Soon afterwards, Shakespeare began publishing work under his name. The evidence is circumstantial, but when considered alongside everything else, it begins to paint a picture of the real author.
Hamlet is Autobiographical:
The story and narrative arc of Shakespeare’s masterpiece align with events and relationships in Oxford’s own life. Lord Burghley, Queen Elizabeth’s chief minister, who Vere lived with as his ward after age twelve is strikingly similar to Polonius. His children, Robert and Anne, bear resemblance to the characters of Laertes and Ophelia.
Oxford was unhappily married to Anne and believed she had a liason behind his back (so much so that he doubted his paternity of their daughter). He, therefore, becomes Hamlet. Hamlet and Oxford are both athletic and poetic. Both loved the theatre, both were captured by pirates, both had fought in sea battles and both had a trusted friend named Horacio (Horace Vere was Oxford’s closest cousin and Ben Jonson was also associated with and translated Horace). In one scene, Hamlet tells Polonius, "Conception is a blessing, but not as your daughter may conceive”, a clear nod to his paternity suspicions.
Given that Hamlet was such a clear expose of Elizabethan court, the fact that Shakespeare wasn't executed for treason indicates that many in the upper-echelons of Elizabethan society likely knew that he wasn't the play's author.