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In this paper, we describe Galois covers of algebraic curves and theirfamilies by using local systems associated to push-forward of sheaves by thestructure morphism. More precisely, if $f:C\to Y$, we consider the sheaves$f_*(\C)$. The group action by the Galois group $G$, yields a decomposition ofthis sheaf into irreducible local systems corresponding to irreduciblerepresentations of the group $G$. If $\rho$ is such an irreduciblerepresentation, the eigensheaf $\L_{\rho}$ of $f_*(\C)$ gives rise to anotheruseful sheaf which is related to the homology group $H_1(C,\C)$. Using this, wedescribe the action of the Galois group $G$ on the homology group. As aparticular example, we study the Dihedral covers of $\P^1$ in some detail.

On Galois Coverings of curves and their Families