Simply put, this book could have some real purpose for someone wanting a gentle introduction into homological algebra if not for one huge blunder. Rotman does do a good job at motivating a lot of the topics and not becoming too longwinded, but there is also an unfortunate fatal flaw in this book as well. This book contains far too many errors to be acceptable. While I acknowledge that all books will contain errors, this amount is beyond a level that should have been allowed to be printed without correction. Some are simple typos that will not affect the average reader. Others, however, will make this book not cater well to its target audience. The pace of this book is too slow as to make it a necessary resource, as Weibel's book of the same title or Kenneth Brown's "Cohomology of Groups" are far more rigorous and complete. This books aim seems to be aimed thus at the graduate level or possibly a mathematician from a different field. However, this audience will be in for a chore. Many mistakes lead to incorrect proofs and even worse incorrect proposition and theorem statements. When trying to understand the functorality of certain constructions, for instance, it is crucial that the reader understand exactly how things work. The mixing up of rings and modules often leaves statements paradoxical. The advanced reader will have no problem finding and fixing these errors, but for those not comfortable in this area of mathematics, this may be a huge challenge. This book may be helpful to some as a secondary resource as it does work out some simpler results that many books (e.g. the ones mentioned above) take for granted. I would not recommend this book for any other reason though.



I will be fair and say that if this book were to receive a major editing job removing most of the errors that it could be a very useful introduction. However, until such a revision is produced, buy a better book.