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Per the title, what are some of the oldest abstract algebra books out there with (unsolved) exercises? Maybe there are some hidden gems from before the 20th century out there. I am already aware of the books of Dickson and van der Waerden.

Squid with Black Bean Sauce
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    In older books (or most non-English language books), the ridiculous "abstract" adjective was not present. – YCor Jul 21 '20 at 17:11
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    @YCor Do you prefer the timeless "modern" instead? – Michael Greinecker Jul 21 '20 at 18:21
  • Isn't it just the meaning of "algebra"? – YCor Jul 21 '20 at 18:55
  • It is also the art of solving equations involving real or complex numbers. – Michael Greinecker Jul 21 '20 at 19:03
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    A year ago you posted a large number of separate questions of this kind, asking for oldest books in various areas of math with exercises (always hoping for "some hidden gems from before the 20th century"). Please consider posting just once a big-list request for the oldest books in different areas of math with exercises, rather than all of these separate questions marching (potentially) through all areas of mathematics that are all the same question. – KConrad Jul 21 '20 at 22:46
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    I agree wirh @KConrad. By the way, it might be just my ignorance, but I have difficulties to see the point of the requirement "with exercises". When you are looking for old books on various subjects, is there a specific reason why you are only interested in books that contain exercises? – Jochen Glueck Jul 21 '20 at 22:53
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    @JochenGlueck see the rationale explained in the post of the earliest question https://mathoverflow.net/questions/313967/reference-request-oldest-linear-algebra-books-with-exercises. It does not explain why there have to be repeated posts about all these different areas of math instead of one single post on the general topic. See also https://mathoverflow.net/questions/327697/reference-request-oldest-number-theory-books-with-unsolved-exercises. – KConrad Jul 21 '20 at 23:13

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For a pre-20th century textbook: Modern Higher Algebra by George Salmon (1876) has exercises (with solutions).

If I may broaden the query from "abstract algebra" to more general "algebra", I note that Elements of Algebra by Euler (1770) has more than one hundred exercises. The exercises are discussed in The origin of the problems in Euler’s algebra.

Here is an example, from the chapter on cubic equations [source].

And another example (find an integer $x$ such that $2x^2-5$ is a cube) [source]

Carlo Beenakker
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Two important early 20th-century abstract algebra textbooks that were superseded by van der Waerden are:

Hasse, H., 1926. Höhre Algebra.

Haupt, O., 1929, Einführung In Die Algebra, Zweiter Band - Mit Einem Anhang Von W. Krull, Akademische Verlagsgesellschaft M. B. H., Leipzig.

For an in-depth historical account of the transition from algebra to abstract algebra (including discussions of the various textbooks) see:

Leo Corry, 1996, Modern Algebra and the Rise of Mathematical Structures, Birkhäuser Verlag.

Philip Ehrlich
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I think the following references might be useful:

H. Weber (1895/1896): Lehrbuch der Algebra, 2 volumes. Vieweg, Braunschweig. It includes examples, but it does not have any separate exercises.

E. Artin (1938): Foundations of Galois Theory. New York University Lecture Notes, New York.

N. Bourbaki (1947): Éléments de Mathématique, Algèbre. Hermann, Paris.

I am not totally sure whether the last two references include exercises.

Mary Sp.
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