At the following website you can read about the Hamlet quartos.
You can also read there the following under the section of Shakespeare's sources:
"Saxo Grammaticus, Danorum Regum Heroumque Historiae (1514). Although this contains all the principal elements of Shakespeare’s plot, it is unlikely that he knew Saxo’s work at first hand."
So it's interesting that Bacon cites this work in the French edition of his Natural History (1631):
“In fact, I have only remarked on a single example of such a marvel, and that is in The History of Denmark, a book written by Saxo Grammaticus, who relates a veritable history that during the reign of King Ericius there arrived at the Court of Denmark a musician very skilled in his profession, who boasted that he could produce the feelings of joy or sadness, of peace or rage, in the breasts of man, by the mere sound of music”.
So readers should consider that maybe 'Shake-Speare' (i.e. Bacon) likely did know of Saxo's work first hand.
more on Saxo's work:
SOURCE FOR HAMLETSAXO GRAMMATICUS. Danorum Regum heroumque historiae. Paris, Iodocus Badius Ascensius, 1514.
Folio, , 198 leaves, roman letter, title printed in large red gothic characters within a renaissance style architectural border in black and red enclosing a woodcut of the Danish king at the head of his army; fine woodcut initials including several specially designed for the book incorporating a portrait of the king of Denmark and the royal arms, etc.; a few inoffensive wormholes throughout, but a clean, crisp copy, bound with two other works (see below) in 17th century blindstamped calf, rebacked in the early 19th century with an attractively gilt spine with green and tan morocco labels.
Rare first edition of this famous history of Denmark, important textually because no complete manuscript version now survives. It was edited by Christiernus Petri, a Canon of Lund. His dedicatory epistle dated “ex Parahisiorum academia, 13.III.1514” is addressed to Lago Bishop of Ruskild. The great interest of the book lies in the fact that it was the principal source for Shakespeare’s Hamlet.
“As a chronicler both of truth and fiction he had in his own land no predecessor, nor had he any literary tradition behind him. Single-handed, therefore, he may be said to have lifted the dead-weight against him, and given Denmark a writer” (Elton, introduction to Saxo Grammaticus). The History is composed from a variety of sources: “Saxo was to Denmark what Geoffrey of Monmouth was to Britain. He drew on Latin histories such as Bede and Adam of Bremen, on Icelandic and Danish MSS. and on oral traditions ... The Amleth saga belongs to a common type of revenge-story in which the hero feigns insanity or stupidity to save his life and gain an opportunity for a coup” (Bullough, Narrative and Dramatic Sources of Shakespeare).
The Amleth story agrees in the main points of its narrative with Shakespeare’s Hamlet: a king is murdered by his brother, who marries the widow and succeeds to the throne. The son of the murdered king feigns madness, whereupon he is suspected and tried, first by entangling him in his love of a maiden (Ophelia), and second by an interview with his mother, during which he discovers and kills a spy (Polonius). The king sends him to Britain in charge of two attendants (Rosencrantz and Guilderstern) with a letter asking for his assassination. He alters the letter so the attendants are slain. Returning to Denmark he kills the courtiers, burns the palace, and slays the king. As Bullough points out, there were considerable changes of plot and emphasis in Shakespeare’s version: “At some stage, the saga already somewhat modernized by Belleforest was brought into line with Renaissance manners and current tales of court-murders and revenge. This involved changing the ending by having Hamlet achieve his vengeance during a fencing match. It also meant altering the way in which Old Hamlet was killed, and the Ghost’s part was made important by substituting the Italianate secret way of poison for open murder at a banquet ... Neither in Saxo or Belleforest did the wicked uncle show any sign of remorse, and the introduction of the prayer scene indicates that the play had religious implications not present in the old saga ...” (ibid.).