Does anyone have any suggestions for abstract algebra books particularly suited to selfstudy?
Here is some background and motivation, if it’s helpful.
I’m currently a junior in high school, but I have some familiarity with groups, rings, polynomials and fields, as I went through Fraleigh’s book. I liked its writing style, but many of the problems were not helpful. I would like to get better at algebra with some other book, particularly one that’s aimed at someone who already has a little familiarity with the objects, but is by no means completely comfortable.
One of my longerterm goals is to learn a bit of algebraic number theory, as I’ve only been studying elementary number theory. That’s why I feel it good to learn more algebra first. (I’d also be interested in suggestions of other good subjects to learn prior to tackling algebraic number theory.)
I was considering using one of Lang’s books, since they seem pretty universal, but I’ve heard rumors that they are very terse and not good for selflearning.
Answer
For Algebra you can look at these books:

Topics in Algebra by I.N. Herstein

Abstract Algebra by Dummit and Foote

Algebra by Michael Artin

Algebra by T.Hungerford (Springer)

Lectures in Abstract Algebra by N.Jacobson (Has 3 volumes!)

Algebra by Anthony Knapp. (2 Volumes.)
My feeling of Herstein is it has lot of problems which are challenging. For theory part i would like to use Dummit and Foote. Artin’s Algebra is very well written and contains a lot of Linear Algebra. Anthony Knapps treatment of Algebra is very comprehensive, and contains a lot of Algebra. Since your aim is to read Algebraic Number Theory you might want to learn some Galois theory also for which there many good books like:

Lectures in Galois theory by Emil Artin

Field theory and its Classical problems by Charles Hadlock.

Galois theory by J.Rotman (Springer.)
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