TITLE: book with lot of examples on abstract algebra and topology
QUESTION [9 upvotes]: I have read a lot of blogs and forums to find out the best of the books on Abstract algebra and Topology but on going through the books I realized that they are full of proofs and all kind of theorems and corollaries.
But the disappointing point is that there are either very small number of examples or none at all to support that particular theorem or proof. My idea of example is practically calculating using a set with contents rather than just saying "a set of integers" and the calculations should go to the end, for example calculating index in subgroups. Everything should be step by step.
I went through "Topics in Algebra" by I.N.Herstein but it's full of rigor. I faced similar problems with topology.
Please help me by suggesting books where I can find lot and lot of simple examples on these topics. Please don't suggest any advanced book but something that keeps me near the base with lot of permutations of ideas.
Even if you have something to suggest other than these, you are most welcome.

REPLY [2 votes]: Dummit and Foote is good for basic finite group theory, which makes sense as the book was written at a time when the classification of finite simple groups was THE big deal in algebra.
That said, I feel like group theory is a lot easier to understand if it's paired with some representation theory from the beginning, and Dummit and Foote doesn't really do much in that regard; as I recall, they only talk about characters (in the sense of one-dimensional representations), and that's relegated to an appendix.
And the section on ring theory seems like more of a forced march through an ever-increasing forest of definitions.  I feel like Aluffi's Algebra: Chapter Zero is an easier read where rings are concerned.
The beginning of Fulton and Harris's Representation Theory, which deals with representations of finite groups, is a good supplement to beginning group theory.