Abstract: 
We present short direct proofs of 
two known properties of complete flat manifolds. 
They say that the diffeomorphism classes of 
$m$-dimensional complete flat manifolds form a 
finite set $S_{CF}(m)$ and that each element of $S_{CF}(m)$ 
is represented by a manifold with finite holonomy group.

1. Institute of Mathematics
   University of Gdañsk
   Wita Stwosza 57
   80-952 Gdañsk, Poland