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.



Oldest abstract algebra book with exercises?
For a pre-20th century textbook: [Modern Higher Algebra](https://archive.org/details/3rdedlessonintro00salmuoft) by George Salmon (1876) has exercises (with solutions).




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If I may broaden the query from "abstract algebra" to more general "algebra", I note that [Elements of Algebra](https://en.wikipedia.org/wiki/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.](http://logica.ugent.be/albrecht/thesis/EulerProblems.ps)


Here is an example, from the chapter on cubic equations
[[source](https://archive.org/details/elementsofalgebr00eule/page/270/mode/2up)].


![](https://ilorentz.org/beenakker/MO/Euler_1770.png)
And another example (find an integer $x$ such that $2x^2-5$ is a cube) [[source](https://reader.digitale-sammlungen.de/de/fs1/object/display/bsb10081749_00575.html)]


![](https://ilorentz.org/beenakker/MO/Euler_1770_2.png)
