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.