I am knowing Abstract Algebra things; I am searching aims of Abstract Algebra and origins of parts of Abstract Algebra. I thought original initial textbooks have explicit links to aims and origins of the parts of Abstract Algebra.

Can we list major textbooks on Abstract Algebra in the order of time?

Abstract Algebra: "In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field." - Wikipedia/AbstractAlgebra

  • $\begingroup$ I don't know what this community thinks of this sort of Q&A, but I've seen on other SE sites that reference-list type Q&A are made Community-Wiki, and just one answer is maintained by the community (unless the answer gets too long and needs to be subdivided). Otherwise, I don't see how to keep the answers in nonoverlapping, chronological order. $\endgroup$
    – Michael E2
    Commented Sep 24, 2023 at 14:24
  • $\begingroup$ The text by van der Waerden was called "Moderne Algebra" (German for "Modern Algebra"). Later editions were called simply "Algebra". It discusses groups, rings, fields, vector spaces, ... $\endgroup$ Commented Sep 25, 2023 at 12:16

1 Answer 1


Notation: BK = Book

BK#1892 The theory of substitution and its applications to algebra. Rev. by the author and translated with his permission by F.N. Cole 1892 (Book was mentioned in preface of BK#1901)

BK#1901 Linear Groups with an Exposition of Galois Field Theory by Dickson L.E. 1901

  • $\begingroup$ archive.org/… $\endgroup$
    – Sensebe
    Commented Sep 24, 2023 at 14:01
  • $\begingroup$ Two english-language books only ? I am almost sure that there were german books (abstract algebra has mainly been developed in Germany). The "Traité des substitutions et des équations algébriques" (1870) by Camille Jordan has been very influential. $\endgroup$ Commented Sep 28, 2023 at 21:09

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