I don't know about the whole book or how it compares to other textbooks, but as someone who didn't really know what exactly Groups, et al. were, I found that first page of Chapter 2 to be very clear and to-the-point. I'm sure not everyone learns the same way, but the way that first page didn't beat around the bush at explaining what Groups, Monoids, and Abelian Groups are seems to really appeal to me.
Then again, maybe I just haven't experienced better material on that topic. Do you have any suggestions?
Short segments of a massive tome can be good! Honestly all decent expositions of groups are basically equally good, though different styles can still appeal more depending on the person.
The problem is when people try to use the whole book for some goal -- whatever that goal is, it's never an efficient route.
Then again, maybe I just haven't experienced better material on that topic. Do you have any suggestions?