An Introduction to the Theory of Groups

Alexandroff is the primary author, but I think of this as Perfect's book, for Hazel Perfect who with the assistance of G M Peterson made the translation from German to English; Lothar Uhlig made the translation from Russian to German. Perfect's translation is a humane and careful presentation of the matter; it is a joy to come under her instruction.

If you are having difficulty in getting started with Group Theory, this will help you, as modern books on the subject usually treat the basics in a rather cursory manner, but the book does not go very far into the theory, and some parts of it have been superseded by clearer explanations.

a proper technical book, well worth the money