Rating: 
Summary: Acceptable introduction to applied group theory.
Review: Cotton's text is infamous for its ease of use and many practical examples. It is ideal for the undergraduate or the chemist who needs only a cursory understanding of group theory. It will get one through the basics, but for serious students, the references contained therein are invaluable.
Rating: 
Summary: Excellent Grad School Reference Text
Review: I used this text as a reference for a grad course in inorganic structure and reactivity. I found it most useful. The explanations were clear, yet not wordy. The exercises at the end of each chapter adequately cover the material. And the character table appendix is invaluable. With appropriate guidance, any student will master the subject.Professor Cotton's expertise in this field of study is well known. The texts he has authored along with the late Prof. Wilkinson have instructed a whole generation of chemists. This text continues that tradition. Any scientist will found this text useful.
Rating: 
Summary: This May Be The Single Most Overrated Text On The Planet
Review: I'm a double major in mathematics and biochemistry at Queens College of CUNY;we're very proud of our excellent,Ivy-League trained chem faculty(which is one of the best kept secrets in academia).I love textbooks and I believe any aspiring scientist must have a substantial libary at thier disposal.That being said; this is the worst textbook I've ever read.The definitions are too terse to be of any use to anybody,the writing is impenetrably dense and the mathematical proofs are careless and unclear.I was taking inorganic chemistry and really struggling with my intro to group theory and symmetry(since I made the mistake of not taking college geometry FIRST with the brilliant Dr.Ravi Kulkarni;that would have made all the difference.Learn from my mistakes;never try and learn mathematical concepts-and this IS a mathematical theory-from a chemist or physicist!)Cotton's book was the only book extant at that time-and it only confused me more.Just goes to show an ugly truth you learn as a college student-a great scientist does NOT a great teacher make.Recently,this dark room of inorganic chemistry was lit up by the brillant book by Robert Carter,"An Introduction To Group Theory And Molecular Symmetry".If you're taking an inorganic chem course at the undergrad or grad levels,run-don't walk-to your bookstore and order this one.And if anybody offers you Cotton,JUST SAY NO!
Rating: 
Summary: no worth buying it!!
Review: Just i would like to give some advice to those who wish to buy this book : think twice before you do it. The problem with this book is not that it is bad, what happens is that it doesnt fit to those you want to have a good theoretical approach to the problem. In fact if you just need it to pass your exam at the university it can really be helpful for it has ,to my mind, an intuitive approach. But if you need to have a deep knowledge about all the mathematical subtilities it isnt the right book (for instance if you want to understand molecular modelling). So,be careful, you may be disappointed with this book...
Rating:
Summary: One Terrible Book
Review: Perhaps for the typical chemist, who has incredible difficulty with arithmetic, this text is appealing and possibly useful, however for those of us who are theorists in this discipline, this book is terrible. It lacks precise definitions of mathematical objects, and contains way too many absolutely ridiculous "brute force" exercises that are worded ambiguously or better yet incorrectly. Additionally, this book is in NO way a substitute for a real algebra text and those chemists who are interested in learning the foundations of group theory and not just the theory of one particular group (i.e. the dihedral group) ought to purchase another book or sit in on an undergraduate course in abstract algebra. After doing so you will find that Cotton's text is a joke.
Rating: 
Summary: Good book for its intended purpose and audience
Review: Professor Cotton's book is a well written introduction to the theory of group representations for chemists. It is appropriate for chemical experimentalists and beginners with a more thoeretical bent. It was NOT INTENDED to be a book of algebra for mathematicians or physicists interested in Lie groups. The pure rotation group is not covered, representations of space groups are not mentioned, ray representations are not used, etc. Many of the reviewers below seem to think they will need one and only one book that deals with applications of group theory - not likely! For a beginner with a background typical of a 1st year grad student in physical or inorganic chemistry at an American university, the book is good. If the complainers below ever tried to teach a course to such students using the more rigorous books they are clamoring for, they would be hung in effigy (if they were lucky).
However, even for the intended audience, there are things that could be improved. Most glaring in my opinion is the treatment of electronic states, as opposed to orbitals. Even "mathematically-challenged chemists" have to face up to Slater determinants as basis functions for multi-electron wavefunctions. The spectroscopy and ligand-field theory topics are obscure if you don't introduce this concept. Symmetry with respect to interchange of particle labels is not that difficult to teach, and is essential for understanding the symmetry requirements that must be placed on electronic and vibrational wave functions.
Rating:
Summary: Good book for its intended purpose and audience
Review: Professor Cotton's book is a well written introduction to the theory of group representations for chemists. It is appropriate for chemical experimentalists and beginners with a more thoeretical bent. It was NOT INTENDED to be a book of algebra for mathematicians or physicists interested in Lie groups. The pure rotation group is not covered, representations of space groups are not mentioned, ray representations are not used, etc. Many of the reviewers below seem to think they will need one and only one book that deals with applications of group theory - not likely! For a beginner with a background typical of a 1st year grad student in physical or inorganic chemistry at an American university, the book is good. If the complainers below ever tried to teach a course to such students using the more rigorous books they are clamoring for, they would be hung in effigy (if they were lucky).
However, even for the intended audience, there are things that could be improved. Most glaring in my opinion is the treatment of electronic states, as opposed to orbitals. Even "mathematically-challenged chemists" have to face up to Slater determinants as basis functions for multi-electron wavefunctions. The spectroscopy and ligand-field theory topics are obscure if you don't introduce this concept. Symmetry with respect to interchange of particle labels is not that difficult to teach, and is essential for understanding the symmetry requirements that must be placed on electronic and vibrational wave functions.
Rating:
Summary: Bad expectations => Bad reviews
Review: So if you are a mathematician or a physicist, don't whine if this book isn't for you. It's for chemists, specifically inorganic ones, who use group theory to analyze ligand chemistry and spectroscopic measurements. It is also useful for those who utilize computational chemistry programs like Gaussian and need to know the basics of orbital and molecular symmetry.
This book contains only point group symmetry and none of the SO, SU, U, etc. groups used in physics. There is also no coverage of Lie algebras.
Rating:
Summary: Bad expectations => Bad reviews
Review: So if you are a mathematician or a physicist, don't whine if this book isn't for you. It's for chemistry, specifically inorganic ones, who use group theory to analyze ligand chemistry and spectroscopy. It is also useful for those who utilize computational chemistry programs like Gaussian and need to know the basics of orbital and molecular symmetry. I'm an organic chemist by trade, and this book is the gold standard for my field.
Rating:
Summary: Good Reference, Poor Textbook
Review: This book is a double edged sword. As a reference textbook for a person who has already had a significant introduction to group theory and chemical applications of it, this book can't be beat. It provides some very detailed mathematical derivations of the theoretical formulas used within group theory which one may not find in an elementary inorganic text which skims over group theory. Additionally, Cotton covers organic, organometallic and inorganic examples which allows the reader to have a broad spectrum of systems to learn from. The blurbs about molecular vibrations and crystallography were nice too. Finally, Cotton does not lack in providing journal references to the original research that he covers in the text. In lieu of all that, this book is a bain to use in order to learn the principles of group theory. Cotton, in his typical fashion, assumes that the reader is well-versed in linear/matrix algebra (and has a very condescending comment for anyone who MIGHT have to read the matrix algebra appendix he has in the back of the text) and that the reader can visualize symmetry operations readily in their head. There are places in the text where he should go into more detail and provide further examples, but he does not. Lastly, anyone who knows anything about group theory knows that it is a pretty dry subject matter. Cotton doesn't enhance the excitement of learning group theory with his dry, humor-less approach to writing the text (not to mention that this 3rd edition is already overdue for another overhauling being over a decade old!). In case you have insomnia while taking your group theory course, attempt to read a full chapter in one sitting, you'll be out cold by the second paragraph! My final verdict, if you are a graduate student in chemistry who already knows something about group theory and its application, but needs a text to jog your memory now and again, this book is worth your money, but if you have to learn the basics of group theory from this book, RUN! Run as fast as you can! Or if you can't do that, buy this book, but buy another book and learn from that one rather than this one.
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