From what little I scrolled, I didn't see any category theory. Just some elementary group theory, point-set topology, real analysis, linear algebra etc Most of it standard material for undergrad math majors.

> And stuff that used to be simple algebra is now explained as something like 'Abelian group linear transformations'.

"Simple algebra" means different things in different professions? For example, Dummit&Foote's Abstract Algebra[0] would be considered "elementary algebra" by most mathematicians. For another example, Principles of Mathematical Analysis by Walter Rudin[1] is "elementary analysis".

[0] https://www.amazon.com/Abstract-Algebra-3rd-David-Dummit/dp/...

[1] https://www.amazon.com/Principles-Mathematical-Analysis-Inte...

The best resource I know of is the textbook I bought for the course I took on group theory and ring theory [1]. It’s pretty expensive and the exercises are very challenging but if you’re a self-motivated student, you can learn a TON of abstract algebra from this one book. You may want to review some linear algebra before you dive in, if you haven’t done so in a while. You can find solutions to many of the exercises online though I can’t vouch for their accuracy.

[1] https://www.amazon.com/Abstract-Algebra-3rd-David-Dummit/dp/...

For self study of abstract algebra, I recommend Dummit & Foote. I used it as a supplement to my undergrad algebra classes and found it to be very useful. This is in contrast to some books like Artin which leave a lot to the readers, while not necessarily bad, are sometimes difficult for self-study.

[0] https://www.amazon.com/Abstract-Algebra-3rd-David-Dummit/dp/...

Most people like the Dummit & Foote book; it tends to be loaded with examples rather than a lot of dense symbolic arguments:

http://www.amazon.com/Abstract-Algebra-Edition-David-Dummit/...

When I learned it, though, it was from this Dover book, which is more affordable:

http://www.amazon.com/Elements-Abstract-Algebra-Dover-Mathem...

I'm soon starting my trek through every problem in the algebra text that Harvard's PhD prelim recommends for study:

Abstract Algebra by Dummit and Foote http://www.amazon.com/Abstract-Algebra-David-S-Dummit/dp/047...

I've started the first section of the first chapter, but that was only in a few hours of spare time. I'll be posting solutions by chapter soon and post my stories/insights on Hacker News. Here's section 1.1 (except the last problem, 36):

http://therobert.org/alg/1.1.pdf

Comments are appreciated. Better now than when I start the real journey. :)