  Gelfand - Na\u{i}mark theorem supplies a one to one correspondence between
commutative $C^*$-algebras and locally compact Hausdorff spaces. So any
noncommutative $C^*$-algebra can be regarded as a generalization of a
topological space. Generalizations of several topological invariants may be
defined by algebraic methods. For example Serre Swan theorem states that
complex topological $K$-theory coincides with $K$-theory of $C^*$-algebras.
This article is concerned with generalization of local systems. The classical
construction of local system implies an existence of a path groupoid. However
the noncommutative geometry does not contain this object. There is a
construction of local system which uses covering projections. Otherwise a
classical (commutative) notion of a covering projection has a noncommutative
generalization. A generalization of noncommutative covering projections
supplies a generalization of local systems.
