There are actually two Third Folios that differ very little from each other. The one in the picture link above is sometimes known as F3b (1664). Here is a link to F3a (1663), the first printing. Several plays added that are probably apocryphal. Boston Public Library.
The last no-name editor Folio, though quartos remained anonymously edited. Rowe, Pope, Hanmer, Warburton, and even Dr. Johnson largely based their editions on F4. Boston Public Library.
Black and Shaaber, Shakespeare's Seventeenth-century Editors, 1632-1685 (1937)
The odd doppelganger of Shakespeare's play is The Taming of a Shrew (1594), of unknown authorship but similar in many particulars. This quarto seems late, but Charles I liked Shakespeare.
Frequently dismissed as a mashup of Shakespeare's sonnets and poems, since the publisher and editor, John Benson, changed pronouns and the ordering of several sonnets or combined them. Yet it is important in reception studies of Shakespeare's nondramatic poetry.
This is a collection of ten quarto play texts that William Jaggard printed for Thomas Pavier in 1619, though some of the title-pages are falsely dated. There are two known volumes in contemporary binding, one at the Folger and the other at Texas Christian University. Other copies of the Pavier editions exist singly. W. W. Greg and others theorized that the collection might have been an early attempt at a Shakespeare collection. Some spurious works (Yorkshire Tragedy, Sir John Oldcastle) are included.