I am a first year undergraduate student majoring in mathematics. Due to the travel ban caused by the Covid-19 outbreak, I am suspending my studies from my uni in the second half of the year (so I have roughly 6-7 months of free time from now). I am planning to teach myself some abstract algebra as well as advanced linear algebra during the break.
More specifically, I am looking for a thorough introduction (and hopefully as general as possible while still being accessible for undergrad) to the basic algebraic objects like groups, rings, fields and vector spaces. The book I am considering to use is Aluffi's Algebra: Chapter 0. This is because the book seems quite comprehensive and self-contained (at least by looking from its table of contents), and the fact that Aluffi introduces categories along the way is also a huge attraction to me that most textbooks don't have.
The thing is, by far I have taken first-year linear algebra, but I have never studied abstract algebra in a systematic manner. I have seen quite a few comments/reviews saying that Aluffi's book is for a second exposure to modern algebra.
So, speaking of my situation, may I ask if Algebra: Chapter 0 can be used as the first book for self-studying abstract algebra (& advanced linear algebra)? And in particular, what would be the pros and cons in doing so?
Any recommendations on other options that may be better than Aluffi's for my situation are also heartily welcomed.