In need of a group theory textbook. I am in need of a group theory textbook for a good summer review. I have already studied from various books (mostly "group theory" part from basic algebra books) and the lecture notes of my teacher, but these notes lack any rigour and are incomplete, while I still have to find a book that can cover all that I've been taught in a way that attracts me. For that reason, any recommendation on group theory books, or online lecture notes would be really appreciated.
 The material that we covered in class was: 
a) actions on groups
b) sylow theorems and applications
c) (semi)products and applications
d) series, solvability, nilpotency
e) introduction to free groups
Thanks a lot in advance.
 A: Although I believe that Dummit and Foote's Abstract Algebra combined with 
Herstein's Topics in Algebra which has excellent exercises is the perfect recipe for the job, I would recommend two more books for the study of finite groups. The first one is Daniel Gorenstein's Finite Groups which is a book of great depth and covers a lot of material about groups. The second one is William Burnside's Theory of Groups of Finite Order (it is available for free).
Some classmates of mine mentioned this book by M. Aschbacher but I have never used it.
I hope that I helped you!

EDIT: I almost forgot. Perhaps the most elegant notes ever written on this subject Group Theory - J.S. Milne.
A: Try these excellent books:


*

*An Introduction to the Theory of Groups by Rotman.

*The Theory of Groups by Marshall Hall Jr.
A: Martin Isaac's book Algebra might be useful to you. It is at the graduate level so it might be useful if you are going through the material a second time.
A: I enjoyed Michael Artin's book Algebra. This would still be as you say the "group theory" part of an abstract algebra book, but it is rigorous and touches on the topics you have listed. 
