Herstein or Herstein?
Answers:
- Neither book is meant as a sequel, they are independent texts.
- The more advanced (and more generally well-accepted) book is Topics in Algebra.
- 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:
- No further comment.
- 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.
- 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.