  We prove that if $M$ and $N$ are Riemannian, oriented $n$-dimensional
manifolds without boundary and additionally $N$ is compact, then Sobolev
mappings $W^{1,n}(M,N)$ of finite distortion are continuous. In particular,
$W^{1,n}(M,N)$ mappings with almost everywhere positive Jacobian are
continuous. This result has been known since 1976 in the case of mappings
$W^{1,n}(\Omega,\mathbb{R}^n)$, where $\Omega\subset\mathbb{R}^n$ is an open
set. The case of mappings between manifolds is much more difficult.
