Algebra, by Michael Artin.
This is the primary textbook.
It will be in the NYU Bookstore, or you can buy it some other way.
Galois Theory, by Emil Artin.
Lectures Delivered at the University of Notre in 1947.
This is a beautiful and historic version of Galios theory
by the guy who invted the approach.
This inexpensive book will be available in the NYU Bookstore.
It is a classic.
Emil Artin is the father of Michael Artin.
Modern Algebra, by Thomas Judson.
Click here for a pdf copy
This was the main text for Honors Algebra I and we will take
problems from it.
Fields and Galois Theory, by J. S. Milne.
This is a clear and professional description of the class
material, at a somewhat higher level than an undergraduate
textbook. Look here for helpful examples.
https://www.jmilne.org/math/CourseNotes/FT.pdf
Topics in Algebra, by I. N. Herstein.
A traditional testbook for math major classes in
abstract algebra.
A Probabilistic Algorithm for Testing Primality, by Michael Rabin.
Click here for a pdf copy.
This is a research paper that introduced and analysed an
algorithm to test whether a number is prime.
Versions of this algorithm happen whenever you do a secure
online transaction.
A Course in Arithmetic, by Jean Pierre-Serre.
Click here for a pdf copy.
"Arithmetic" is a mistranslation of the French title, which refers to number theory, not
what Americans call arithmetic.
We will use this as a reference for its treatment of finite fields and the proof of
the quadratic reciprocity theorem.
Linear Representations of Finite Groups, by Jean Pierre-Serre.
Click here for a pdf copy.
The link should work for any registered NYU student.
This is a beautiful classic book on group representation theory.