  These notes provide an exposition on obtaining the well-known standard
results of quasiregular maps on Riemannian manifolds, given the corresponding
theory in the Euclidean setting. We recall several different approaches to
first-order Sobolev spaces between Riemannian manifolds, and show that they
result in equivalent definitions of quasiregular maps. We explain how e.g.
Reshetnyak's theorem, degree and local index theory, and the quasiregular
change of variables formula are transferred into the manifold setting from
Euclidean spaces. Finally, we conclude with a proof of the basic fact that
pull-backs with quasiregular maps preserve Sobolev differential forms of the
conformal exponent
