An Introduction to the Theory of Groups

Rating:
Summary: Fun but not easy
Review: I am not sure I would take this specific book to a desert island but I would highly recommend it to anyone who is in possession of patience, self-motivation and willingness to spend time working through both the problems and any gaps that may occur within the proofs. This book can be used both by Graduate students or as a topics/independent study course for well prepared and motivated undergraduates.
In general, you can be guaranteed that the exposition present within any book by Rotman is par-excellence and this book is no exception. The material is presented in a sound and definite logical manner, which results in gently directing the reader through an 'introduction' to group theory by presenting the material in well thought out and bite sized portions. The only negative aspect of this book, which is minimal as best, is the authors choice of notation, for example the notation used to define G-sets in chapter 3 does not necessarily do the topic justice since G-sets in their own right are an important concept. But, as stated, this is the only complaint and is easily remedied. Enjoy!

Rating:
Summary: Solid, but occasionally frustrating
Review: I used this book as a means of writing my senior thesis on the clasification of the projective unimodular groups and the Mathieu groups as being simple. Most of the proofs were well constructed and easy to follow. What this books lacks is a proof reading. Several of the proofs make no sense in the form in which they are written. Also, his notation at times becomes cluttered and not easy to follow. One can imagine how difficult notation can be in general, but when it is full of typographical errors, it can be almost impossible to wade through without the help of someone who knows the material. This book is certainly not a waste of time to read and is very good as a reference for theorems concerning finite groups, however do not put all your eggs in one basket and base your education on this one book.

Rating:
Summary: Good book but many errors
Review: This is a good book, well-organized and contains many useful materials. However I do not recommend it as an independent study textbook (which is what I did). There are many errors, most of them are typographical but some of them are wrong numbers which are very difficult to correct, especially in the exercises given. And the exercises are very important -- the following discussions and proofs depend on some of them. Springer published a "corrected second printing" in 1999 but obviously they didn't do a good job (I purchased the new one and I got the old one in the library).