A Stein manifold is a complex manifold which admits a proper

holomorphic embedding into a complex Euclidean space. Examples

include open Riemann surfaces and domains of holomorphy over $C^n$.

Every n-dimensional Stein manifold admits a holomorphic immersion

into $C^k$ with $k=[3n/2]$, but in general not to a lower dimensional

space. In this talk I will discuss progress on the following

outstanding classical problem:

Does every n-dimensional Stein manifold with trivial tangent bundle

admit a holomorphic immersion to $C^n$ ?