Shakespeare's manuscripts
With the possible exception of a few pages of Sir Thomas More, a play that Shakespeare may have helped write, no manuscripts of Shakespeare's survive. The only certain evidence we have of his handwriting is his signature.
From it we know that Shakespeare wrote in the older "secretary" hand rather than the newer italic script, which is more like today's.
Before printing, the play was often transcribed by a scribe (one has been identified, a certain Ralph Crane). The copy for the printer was thus clear, but less informative* than the originals.
There were probably several manuscript versions of a given play. As well as scribal transcripts, an author may have provided a fair copy to the actors, or a rougher draft sometimes known as the "foul papers"; several of the plays may have been printed directly from drafts of this kind.
Why "foul"?
A manuscript of this kind might include deleted material, false starts, and other inaccuracies, and the handwriting would be less readable than a scribe's--hence it would be difficult for the compositors to set the type.
But there would also be information valuable to the scholar or the modern reader: Shakespeare sometimes uses an actor's name instead of the character's name, for example, so we learn not only who acted the part, but that the part was conceived for a particular style of performance.
There may also be stage directions that Shakespeare inserted for the benefit of the actors (official manuscripts seldom included stage directions). In Antony and Cleopatra, possibly printed from Shakespeare's foul papers, there is a stage direction, after Cleopatra says of the Messenger, "Rogue, thou hast lived too long": "Draw a knife" -- and without it we would not otherwise know that she did so.
A possible revision
Fascinating examples of what may be Shakespeare's revisions of his work have been preserved in Love's Labour's Lost, since the compositor seems accidentally to have included both the original and the rewritten passages.
The young lord Berowne justifies their breaking of a vow to study for three years without seeing women. In the first version this is what he says:
From women's eyes this doctrine I derive:
They are the ground, the books, the academ[i]es,
From whence doth spring the true Promethean fire.
(4.3.299-301)
(Prometheus was the mortal who stole fire from the Gods.)
In the revised version, the lines have been expanded:
From women's eyes this doctrine I derive:
They sparkle still the right Promethean fire;
They are the books, the arts, the academ[i]es,
That show, contain, and nourish all the world;
Else none at all in aught proves excellent.
(4.3.347-51)
The second version heightens meaning by the use of more intense verbs ("sparkle," "nourish"), and further exaggerates Berowne's rationalization by even greater hyperbole.
There has been some interesting and extensive debate in recent years about the extent to which Shakespeare revised his own plays. Some scholars contend that the widely differing versions of King Lear (published in 1608 and 1623) especially show signs of careful revision.
Footnotes
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Less informative. . .
Scribal copies tended to include fewer stage directions and to make the text more "literary" rather than to provide an acting version. They were also less accurate, since there is always the probability of errors in transcription (passages misread, or omitted entirely as the scribe's eye picks up the same word later in the passage.