What were Shakespeare's sources?

Shakespeare’s primary source appears to be Edward Hall’s The Union of the Two Noble and Illustrate Families of Lancastre and Yorke published in 1548 that included Sir Thomas More’s “The Tragical Doynges of Kyng Richard the Thirde.” Other sources include The Third Volume of Chronicles by Raphael Holinshed for details on the action and The Mirour for Magistrates, both dating from 1587.
In Shadowplay, Clare Asquith also argues that Richard III was most likely a parody of Elizabeth’s closest councilor and Secretary of State, Robert Cecil. Not only did Richard’s hunchback mock Cecil’s own physical appearance and mannerisms, but Richard’s opening speech also describes Cecil’s political career. Many descriptions of Richard throughout the text appear to be specific references to Cecil, such as his nickname “Elf” or his association with the secret service, a “black intelligencer” (RIII 4.4.71). However, Shakespeare’s cunning layering of symbolism of Richard as a Vice figure as well helps him to subtly escape criticism, just as he does in Richard II, about which Elizabeth famously remarked “I am Richard II, know ye not that?” Despite the “ruthless and efficient propaganda machine in place” that the transmission of “politically correct versions of national history,” Shakespeare circumvented Elizabeth’s disapproval with his talent and clever use of coded meaning.

References:

Asquith, Clare. Shadowplay. NY: Public Affairs. 2005.

Hattaway, Michael. Cambridge Companion to Shakespeare’s History Plays. Cambridge University Press. 2002. p.103