Herstein or Herstein?

Answers:

  1. Neither book is meant as a sequel, they are independent texts.
  2. The more advanced (and more generally well-accepted) book is Topics in Algebra.
  3. It's always a good idea to read more (especially in mathematics), but generally I would advise (a) to read more than one author and (b) to read something other than Herstein's Abstract Algebra.

Additional comments, respectively:

  1. No further comment.
  2. I don't know of any occasion where somebody has referred to an algebra book as "Herstein" and has been referring to Abstract Algebra - they always mean Topics in Algebra. To add to this point, Topics in Algebra is highly recommended on the Chicago undergraduate mathematics bibliography, while Abstract Algebra isn't mentioned.
  3. If you're looking towards graduate studies, you might want to check out Abstract Algebra by Dummit/Foote instead. If that's too heavy (also, perhaps too hard at this stage), an oft-recommended text is Fraleigh's A First Course in Abstract Algebra.

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Book Recommendation

Abstract Algebra

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