My second abstract algebra class had no lecture notes, and the textbook was Robinson's A Course in the Theory of Groups. I couldn't get through even the first chapter of this book, so my professor recommended that I read this book by Rotman instead. The structure of things in algebra started making much more sense to me. I was able to understand much better what was going on in class and the motivation for what we studied. Though it's self-contained, I'd recommend this as a book for self-study once you've already got a handle on the basics of algebra. The exercises are tricky but doable, and the way the book is structured, it is essential to read them to understand the arguments. Some proofs depend on solutions to exercises.