I presume this is a GAGA-style result, but I cannot find a reference.



Why are Stein manifolds/spaces the analog of affine varieties/schemes in algebraic geometry?
Also like affine varieties, we have:



> 
> Theorem. A complex manifold is Stein if and only if it embeds into some $\mathbb{C}^N$ as a closed complex submanifold.
> 
> 
> 


For the "only if" direction, see Hörmander, *An Introduction to Complex Analysis in Several variables*, Theorem 5.3.9. For the converse, an argument is contained on pp 109-110 of Hörmander, immediately after the definition of Stein manifold.


