I am studying spaces of the form $C^{k}(\mathcal{M},\mathcal{N})$ between manifolds ($k=\infty$ allowed) and I am looking for extensive references, especially analysing their topology and smooth structure.
I know that there are two choices of topologies, namely the "compact open $C^k$" and "Whitney $C^k$ topology“ and they agree in case $\mathcal{M}$ is compact. Furthermore, these spaces are Banach manifolds if $k$ finite. I am looking for references discussing these structures explicitly and in all the necessary details. I good book seems to be the second chapter of Hirsch's "Differential topology", but it is unfortunately rather short and he does not talk about the smooth structure of these spaces. The classical textbooks by Michor and Kriegl-Michor are also very nice, but I am looking for a more practical treatment, as these books are very abstract, i.e. they define the topologies using Jet bundles, which is of course interesting, but I would like to have a more "elementary" treatment, for example using charts or bases of these topologies, like in Hirsch.
