TITLE: Is Aluffi's "Algebra: Chapter 0" a good introduction to algebra?
QUESTION [45 upvotes]: I'm teaching myself following Algebra: Chapter 0 and up until now (I'm at chapter 3) I'm enjoying myself. In spite of that I have some doubts.

It's not a standard text. All of the category theory, although I really like it, makes me feel like I'm not learning the "serious" algebra the way it supposed to be learned. 
So far the exercises are not particularly challenging. This worries me because I'm not a student at any university and I have no mathematician friends to talk to and so the only way for me to check my level of understanding is doing the exercises. 
From what I looked most of the courses on algebra contain materials such as Galois theory and representation theory which to my understanding are not present in this book.

I have a copy of Artin's Algebra as well but I didn’t like it as much, although I understand it's very popular. Should I switch to that book? Ir maybe to a another book entirely?

REPLY [5 votes]: Saal, I second the opinion, based on starting the book, that Aluffi has one of the most user-friendly intros to category theory around. And that is a very good thing because one can relatively easily make one's way through the basics of abstract algebra then hit the wall of categorical thinking and get lost and discouraged. And given its importance as well, it is very nice that you seem to be getting it.
As others as pointed out, if you want more on group representations, you can look at Dummit and Foote, or Lang, and I'm sure Jacobson's Basic Algebra (yes, it has long chapters on Galois Theory in vol. 1 and Rep. Theory in vol. 2). Also, Emil Artin's little book on Galois Theory I recall as being very concise and clear. 
Indeed, if you want something that is a bit more 'concrete,' and less concerned with arrows and diagrams, then in increasing order of difficulty, these are excellent books. I am currently concentrating on Dummit and Foote while starting to look at Aluffi for decent insight:

Birkhoff and MacLane, Survey of Modern Algebra. 4th edition very nice. Undergrad level.
Herstein, Topics in Algebra. Intermediate in level between undergrad and grad. Beautifully written.
Dummit and Foote, Abstract Algebra. Excellent. Has some of the topics Aluffi leaves out.

I find Artin's Algebra and bit quirky, and he leaves out proof details I'd like to see sometimes. Lang's Algebra is also quirky, but interesting and encyclopedic.