I'm looking for books which have a good portion on Surfaces. I know Hatcher's Algebraic Topology has a decent part where he does venture into them. But I was looking for something more, surfaces + covering maps etc. Something that would give me the tools necessary to approach and answer questions like these: Covering map between orientable compact connected surfaces without boundary with genus g and An example of non-homeomorphic surfaces, S1,S2, such that S1×[0,1] is homeomorphic to S2×[0,1]
I have been unable to find a good (algebraic) topology book which does that. Any recommendations are helpful!