  This is an overview article. After an introduction to convenient calculus in
infinite dimensions, the foundational material for manifolds of mappings is
presented. The central character is the smooth convenient manifold
$C^{\infty}(M,N)$ of all smooth mappings from a finite dimensional Whitney
manifold germ $M$ into a smooth manifold $N$. A Whitney manifold germ is a
smooth (in the interior) manifold with a very general boundary, but still
admitting a continuous Whitney extension operator. This notion is developed
here for the needs of geometric continuum mechanics.
