A good book for beginning Group theory

Solution 1:

Perhaps A Book of Abstract Algebra by Charles Pinter? It's very cheap, and if I remember correctly, provides motivation for the theorems/corollaries/etc. It's a small book, and there's a lot of stuff it doesn't cover, but I think it would prepare the reader well for more advanced treatments of algebra.

Solution 2:

"A first course in Abstract Algebra" by Fraleigh is a great introduction to Algebra and it is packed with examples. My experience with this book is I learned Algebra on my own out of the first half of this book and took a course out of the second half. It is also available for free online if cost is a factor.