Reddit mentions of Contemporary Abstract Algebra

Any introductory abstract algebra book will have the basics of of rings, ideals, and quotient rings, as well as a few other things.

My class on intro to group theory used Gallian's Contemporary Abstract Algebra, which I'm a pretty big fan of as an introduction. It's gentle and doesn't rush into things, but has a large amount of exercises, some of which will really stretch your understanding.

If you want something a little harder, but a little deeper, Artin's Algebra is very popular, and for very good reason. It'll help you develop your group theory knowledge as well.

I would actually recommend: Contemporary Abstract Algebra.


I used A First Course in Abstract Algebra and Contemporary Algebra for Rings/Fields and Groups, respectively. Contemporary Abstract Algebra is a much easier read with lots of examples and more easier problems for someone at your level to work with. It also has many, many more problems per section and a lot more answers.

A First Course in Abstract Algebra is a fine textbook, but maybe a bit beyond your level right now being a high school student -- that's not a bad thing.

Also do not even think about reading the Galois theory sections of these textbooks. They do it in an extremely poor manner and I think A First Course in Abstract Algebra even leaves out a certain type of Field extension which is actually required to define a Galois extension, effectively cutting out an important chunk of Galois theory. They end up using specific irreducible polynomials to avoid running into problems with the way they do it.

Contemporary Abstract Algebra by James Gallian https://www.amazon.com/Contemporary-Abstract-Algebra-Joseph-Gallian/dp/1133599702

Gallian is a good intro:

https://www.amazon.com/Contemporary-Abstract-Algebra-Joseph-Gallian/dp/1133599702

Doesn't require to much background, but is a good intro to the subject. D&F is a great book, but feels more referency