  Let $C$ be an arrangement of affine hyperplanes in a complex affine space
$X$, $D$ the ring of algebraic differential operators on $X$. We define a
category of quivers associated with $C$. A quiver is a collection of vector
spaces, attached to strata of the arrangement, and suitable linear maps between
the vector spaces . To a quiver we assign a $D$-module on $X$, called the
quiver $D$-module. We describe basic operations for $D$-modules in terms of
linear algebra of quivers. We give an explicit construction of a free
resolution of a quive $D$-module and use the construction to describe the
associated perverse sheaf. As an application, we calculate the cohomology of
$X$ with coefficients in the quiver perverse sheaf (under certain assumptions).
