  The paper deals with $C^*$-algebras generated by a net of Hilbert spaces over
a partially ordered set.
  The family of those algebras constitutes a net of $C^*$-algebras over the
same set. It is shown that every such an algebra is graded by the first
homotopy group of the partially ordered set. We consider inductive systems of
$C^*$-algebras and their limits over maximal directed subsets. We also study
properties of morphisms for nets of Hilbert spaces as well as nets of
$C^*$-algebras.
