"The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics."
Categories are not a good way to be introduced to the "main topics" of abstract algebra. Yes, Category Theory can be seen as the "Chapter 0" of a course on abstract algebra, but for beginners a traditional presentation based on sets would be much easier to digest.
There is a similarity between using categories and using functional programming style or a language - as opposed to using an approach to mathematics based on sets and using the imperative programming style or a language: the latter is just more intuitive and therefore easier to learn for a beginner.
If you read the referenced book, you'd know the author does exactly this.
The book doesn't really require much knowledge.
If you either already have a math degree, or if you're already at the point where you're ready to take an upper-level undergraduate math course, then it may be a decent book for you. Maybe. For example, if you're:
- already very comfortable with linear algebra
- possibly been exposed to a bit of topology in analysis class
- already been exposed to abstract algebra a bit by a more theoretical approach to linear algebra (comfortable with proving things in linear algebra via vector spaces and fields)
Otherwise, I would absolutely steer clear of it. The writing style is also not terribly beginner-friendly, in my opinion.
The closest book I can think of to what you're asking for would be "Conceptual Mathematics: A First Introduction to Categories". Though obviously I don't know whether it's a good fit for your particular background and learning style.