A local system on a topological space is a locally constant sheaf. A finite-rank local system of vector spaces over a fixed field on a connected, locally path-connected, locally simply connected topological space is equivalently a group representation of its fundamental group over that field, after choosing a basepoint. Transport around loops gives the group representation, called monodromy. On a simply connected topological space satisfying these local conditions, such a local system is constant.
In the étale setting, a lisse sheaf is the analogous 
-adic
coefficient object. On a connected normal
variety over a field of characteristic
different from 
, a lisse
sheaf with coefficient field a finite
extension 
of 
corresponds to a continuous group representation of the étale
fundamental group on a finite-dimensional 
-vector space (Milne 2013,
pp. 124-126). The geometric
Langlands correspondence uses local systems for the Langlands
dual group as spectral parameters.
