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Algebra (3rd ed.)

Description

Serge Lang was a French mathematician and prolific writer of math books at all levels. This is his most famous work.

discusses Noether (ch. 10), Galois theory (ch. 6), etc.

The only downside of Lang is that he's a Bourbakian.

Gilmore 2008 (ch 1) references this book for its treatment of Galois's solution to cubics, quartics, quintics, etc.