It is difficult to catalogue historical information about the lute, because much important information about the lute and lute playing is scattered in manuscripts, and brief introductions to printed books of music.
A list of relevant treatises, with or without tablatures, in chronological order of publication, and in some cases with downloadable facsimiles, can be found at the Lute Library, web.archive.org/web/20151227165832/www.lutelibrary.com/treatises
The most important printed sources, mostly for lute and mostly including tablature are: Annotated catalogue of historical printed sources 1511 Virdung, 1512 Schlick, 1523 Judenkunig, 1528 Agricola, 1529 Vorsterman, Attaignant, 1530 Oronce Fine, 1532 Gerle, 1535 Ganassi, 1540 Pagano, 1543 Ganassi, 1549 and 1555 Bermudo, 1556 Discours non plus melancholique, 1557 Henestrosa, 1565 Tomas de Sancta Maria, 1568, 1569 and 1581, 1584, Galilei, 1568 and 1574 Le Roy, 1601 Cerreto, 1603, 1607 and 1617 Besard, 1603, Robinson, 1607 Aggazzari, 1610 Robert Dowland, 1615 and 1618 Vallet, 1619 and 1620 Praetorius, 1623 Piccinini, 1626, 1701 and 1735 Amat, 1636, 1637, 1648 Mersenne, 1640 Velasco, 1647 Foscarini, 1650 Kircher, 1660 Fleury, 1666 Nivers, Playford, 1669 Bartolotti, 1672 Salmon, 1674 and 1697 Sanz, 1676 Asioli, Mace, 1677 Ribayaz, 1679 Perrine, 1680 Grenerin, Matteis, Micheli, 1682 Matteis, 1682, 1683 and 1698, Perrine, 1690 Delair, 1690 and 1699 Derosiers, 1695, 1735 Le Sage de Richee, 1701 Sauveur, 1703, 1705, 1708, 1710, Brossard, 1713 and 1727 Mattheson, 1714 Santiago de Murcia, 1716 and 1730 Campion, 1723 Bonanni, 1724 Nassarre, 1727 Baron, 1732 Kellner, 1732 and 1741 Majer, Walther, 1737 and 1749 Christoph, 1740 Grassineua, Weigel, 1752 Quantz, 1757 Seidel.
And manuscript sources: Annotated catalogue of historical lute manuscripts 1510s Capirola, 1630s Stobaeus, 1660s Burwell, 1700s Talbot, 1729 Le Cocq.
An increasing number of early printed books can be found in facsimile or older editions at www.archive.org, Project Gutenburg www.gutenberg.org/, and the Online Books page: onlinebooks.library.upenn.edu/ Many important English sources can be found at EEBO, Early English Books Online: eebo.chadwyck.com/home. French sources can be found at the Bibliotheque Nationale de France site www.bnf.fr/fr/acc/x.accueil.html and the Gallica website gallica.bnf.fr/?lang=en Hispanic sources can be found at Biblioteca Digital Hispanica www.bne.es/en/Catalogos/BibliotecaDigitalHispanica/Inicio/
Bernd Haegemann's links to writings on historical performance practice www.symbol4.de/theory.htm
Some of the most important historical sources not containing tablature are as follows, in roughly chronological order:
Tinctoris, De inventione et usu musicae, online at Indiana university site: www.chmtl.indiana.edu/tml/15th/TININV4_TEXT.html
A broadside lute instruction, on Kenneth Sparr’s website: www.tabulatura.com/PAGANO.HTM
Agazzari 1606, writings on continuo: www.cs.helsinki.fi/u/wikla/mus/agazzari.html
Dispute between the lute and guitar, in Charles Sorel, Nouveau Receuil . . . (1644): gallica.bnf.fr/ark:/12148/bpt6k715706/f4.image.r=charles%20sorel,%20nouveau%20recueil.langEN
Salmon's Essay on the Advancement of Music (1672): digital.nls.uk/special-collections-of-printed-music/pageturner.cfm?id=94569500
An early 18th century Swedish Lute Tutor: www.tabulatura.com/TUTOR2.HTM