Book recommendation: Constructing diffeomorphisms / homeomorphisms (elementary differential geometry)

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Sorry for the vague title, i didn't know how to phrase it correctly. I noticed that i have a very hard time whenever it comes to finding explicit diffeomorphisms or homeomorphisms rather than proof by picture or hand waving arguments. I assume that this has also to do with my lack of exposure to elementary geometry courses in the past.

I stumbled upon this question: How to deal with hoemomorphisms

which is essentially exactly what i mean.

However, i figured that this is barely something that can be covered in a single Q&A, thus i wanted to ask if anyone happens to know some good books that would fit my needs.

I really do not know what exactly to look for. Elementary geometry books? Undergraduate level Differential geometry books?

I would really appreciate any recommendation.