Reference requestion: Existence/construction of bump functions

Question

I'm not much of an analyst myself, but I've time and time again come across proofs which require knowledge of the existence of bump functions. However, I've never studied them, so I'm missing important facts such as what specifications one can make and still be guaranteed the existence of a bump function, and what spaces one can construct bump functions on. What sort of text/chapters should I read to get a quick introduction to the subject and a proof of some important existence theorems pertaining to this?

Answer 1

In my case, the reference which turned out to me most useful to me is Lee's Introduction to Smooth Manifolds, 2nd ed., Chapter 2.