Textbooks for learning Algebraic Topology

Question

No doubt a similar question has been answered before, but I make my ideal textbook specific.

Does anyone know of an Algebraic Topology textbook with the following properties.

-Accessible (Nothing Hardcore Please, I would consider myself a very average student)

-Solutions (They need not be worked solutions, although that would be nice, even one liners telling me solutions to more computational questions would be really nice)

-I am currently working through Munkres' Algebraic Topology, It is accessible but has no solutions so it is very frustrating when I need to check whether or not I computed the homology group of the connected sum of a double tori correctly or not, and the like.

-On that note, for the connected sum of two tori is $H_{1}(T\#T)=Z \oplus Z \oplus Z \oplus Z$? and $H_{2}(T\# T)=Z$. No working needed, unless you really want to....

Answer 1

I guess the Fulton (Algebraic Topology, a first course) would be a good choice. He stays quite elementary throughout the book, and there are hints for most exercices at the end.

Answer 2

Check out From Calculus to Cohomology by Madsen. Here is the link

http://www.amazon.com/From-Calculus-Cohomology-Characteristic-Classes/dp/0521589568

It is at a lower level than Munkres and has some good simple examples. All the exercises are at the end of the book. Unfortunately there are no solutions, but there are a fair amount of hints.

Also Introduction to Topological Manifolds by Lee has some nice material in it.

http://www.amazon.com/Introduction-Topological-Manifolds-Graduate-Mathematics/dp/1461427908/ref=sr_1_2?s=books&ie=UTF8&qid=1458733673&sr=1-2&keywords=introduction+to+topological+manifolds

When I learned the subject I found the background I learned from Lee's book very helpful when I read Munkres. Once again no solutions, but the authors exposition is second to none.

Answer 3

Elementary Topology Problem Textbook by Viro, Harlamov, etc. as an introduction It covers only part of a subject, but it has solutions.