The he earliest one seems to be
C. Jordan, Traite des substitutions algebriques:
C. Jordan, Traite des substitutions et des equations algebriques. (French)
Paris. Gauthier-Villars. 1870. Published: 1870
The most comprehensive one covering this period is
Dickson, Linear groups with an exposition of the Galois field theory. (German)
Leipzig: B. G. Teubner. X + 312 S. (Teubners Sammlung No. VI.) Published: 1901
If you are also interested in papers, read C. Jordan, for example,
Memoire sur les groupes des mouvements.
Brioschi Ann. (2). II. 168-215. 320-345. Published: 1868
and Oeuvres Complete of Lie and Killing, Also Cartan:
Cartan, E.
Sur la structure des groupes de transformations finis et continus. (French)
These presentee a la Faculte des Sciences. 156 S. Paris. Nony et Co. Published: 1894,
Sur la reduction a sa forme canonique de la structure d'un groupe de transformations fini et continu. (French)
American J. 18, 1-61. Published: 1896
Beside this, papers of
Arthur Cayley, Sylov, Holder, Mattheu, Klein, Burnside and Frobenius.
To find their papers use Jahrbuch database,
http://www.emis.de/cgi-bin/jfmen/MATH/JFM/full.html
which is available free on Internet, unlike Mathscinet and Zentralblatt, and covers the late 19s century very well.