Algebra 
in the Long Nineteenth Century.
Most material in Net Advance Retro
antedates 1920. It may be obsolete or incorrect. 
 
- General:
- Leçons élémentaires sur 
les mathematiques (1795) 
by Joseph-Louis Lagrange. English translation:
Lectures on Elementary Mathematics 
[Chicago: Open Court, 1898]
 -  
Leçons de mathématiques
donneées a l'École Normale en 1795
 by Pierre Simon Laplace
[Journal de l'École Polytechnique , VII & VIII (1812)]
 - 
Traité de la résolution
des équations numériques de tous les degrés
by Joseph-Louis Lagrange
[Paris: Courcier, 1808]
 - 
Leçons sur le Calcul des Fonctions
by Joseph-Louis Lagrange
[Paris: Courcier, 1806]
 - 
Elements of Algebra by Leonhard Euler [London: Longman, Rees, Orme, 1828].
With notes by Bernoulli and additions by Lagrange.
  
 - 
A Syllabus of Algebra
 by Henry Pearson 
[Cambridge: Hall, 1833].
 - 
Elements of Algebra Preliminary to the Differential Calculus
by Augustus De Morgan
[London: Taylor and Walton, 1837]
 - 
Trigonometry and Double Algebra
by Augustus De Morgan
[London: Taylor, Walton, and Maberly, 1849]
"The term double algebra ... means algebra in which
each symbol stands for an object of thought having two
distinct and independent qualities ... If by the application
of a somewhat startling adjective, any of those who are
still bewildered by an art in which impossible quantities
are made objects of reasoning should become aware that the art has 
become a science, and the impossibilities possible, they, at
least, will have no objection to the phrase."
 - 
A University Algebra
 by Edward Olney
[New York: Sheldon, 1885].
 - 
Academic Algebra
 by William J. Milne
[New York: American Book Co., 1901]. High-school level.
  
 - 
Graphic Algebra
 by Arthur Schultze
[New York: Macmillan, 1922] 
Meaning basic algebra with numerous illustrative graphs, almost like a computerised modern course.
  
 
 - Aspects:
MATRICES;
 - Aspects: EQUATION THEORY (see also 
Matrices):
 - Aspects: EXTREMA without calculus:
 - Aspects: NOTATION:
 - Aspects: SUMMATIONS and EXTENDED PRODUCTS: