Good book for algebra after Herstein? What is a good book to read after herstein's topics in algebra?
I've read in reviews somewhere that it's a bit shallow...
The main interests are algebraic and differential geometry. I prefer books with challenging excersices.
Something that crossed my mind: prehaps
 it's preferable that I should learn different topics from different books? 

I would like to recommend 'Algebra' by T Hungerford. After learning some commutative algebra, you may like to pursue Homological Algebra from say Weibel or Rotman (since you are interested in learning Algebraic geometry). And for learning more about commutative algebra you may like to see the books by Matsumura or Kaplansky. 
There is also a comprehensive 2 volume book on Algebra by Nathan Jacobson. 
