  Let $M$ be a closed manifold and let $N$ be a connected manifold without
boundary. For each $k\in\mathbb{N}$ the set of $k$ times continuously
differentiable maps between $M$ and $N$ has the structure of a smooth Banach
manifold where the underlying manifold topology is the compact-open $C^k$
topology. We provide a detailed and rigorous proof for this important statement
which is already partially covered by existing literature.
