TITLE: Visualising algebraic topology
QUESTION [2 upvotes]: I'm new to algebraic topology and although I can follow the arguments it would be nice to be able to visualise important concepts like homology and excision. 
Can anyone recommend a book or other source that approaches these concepts in a visual, rather than a simply formal, way?

REPLY [2 votes]: I had a similar experience when I took algebraic topology. The thing that worked best for me was to actually do all the exercises that Hatcher provided. While many would say this is largely unnecessary, and it takes a lot of time, I felt it was worth it. Algebraic topology is a new way of thinking and therefore we need to spend a lot of time with the subject. Time best spent, in my opinion, doing exercises and investigating the conditions of the theorems, propositions, lemmas and corollaries. 
Hatcher has plenty of exercises and it is possible to do all of them. I completed every exercise from Chapters 1-3 within the span of a semester. 
Hope this helps.
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