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This is mostly adressed to those who has studied the book. I've heard a lot about this particular book and browsed it's contents. However, I would like to be certain whether I will encounter some facts I would have to take for granted or from other sources. From the preface:

This book was written with the idea that it would be used by students in their first year or two of graduate school. It is assumed that the reader is familiar with basic algebraic concepts such as groups and rings. It as also assumed that the student has an introductory course in topology.

Now, I would like to know how well one should know group and ring theory(and modules too, I assume? ) and general topology.

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  • $\begingroup$ Perhaps you could just scan the book for when some algebraic notions are introduced. $\endgroup$ – Kevin Carlson Sep 20 '15 at 18:24
  • $\begingroup$ Unfortunately, I don't have such copy where you can search words. $\endgroup$ – JDou9 Sep 22 '15 at 19:25
  • $\begingroup$ I mean to actually look through the book, or in the index. $\endgroup$ – Kevin Carlson Sep 22 '15 at 22:55
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The first 20 or so chapters of the book are largely accessible to someone who understands what groups and rings are and has a solid understanding of the kernel and image of a homomorphism. At some points you will need to know what is meant by a tensor product of modules, and what is meant by an algebra, but this is included in an appendix.

The point-set topological background required is fairly minimal, and is used only to set up the machinery of homotopy theory that is the main focus of the book. You should have a solid understanding of compactness, (path)-connectedness, and what it means to be a Hausdorff space before approaching this book.

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