  We establish Luzin N and Morse--Sard properties for functions from the
Sobolev space $W^{n,1}({\mathbb R}^{n})$. Using these results we prove that
almost all level sets are finite disjoint unions of $C^1$--smooth compact
manifolds of dimension $n-1$. These results remain valid also within the larger
space of functions of bounded variation $BV_{n}({\mathbb R}^{n})$. For the
proofs we establish and use some new results on Luzin--type approximation of
Sobolev and BV--functions by $C^k$--functions, where the exceptional sets have
small Hausdorff content.
