I am entering a Ph.D. program in pure math this fall. Over the summer, I am hoping to review the basics of algebraic topology (fundamental group, covering space theory, etc.) and I wondered if you had a particular source you would recommend for that. I'm looking for a book that has a lot of good exercises, and serves as a thorough and intuitive explication of the topics for someone who later wants to study them more deeply.
I already own (little) Munkres, Lee's Introduction to Topological Manifolds, and the two little books by Milnor and Wallace, and I may use those as sources. I also own Hatcher's text, but that is a bit too advanced for this task. I wanted to choose well, because I think a good source can make all the difference.
What do you think?