  A maximal surface $\sb$ with isolated singularities in a complete flat
Lorentzian 3-manifold $\N$ is said to be entire if it lifts to a (periodic)
entire multigraph $\tilde{\sb}$ in $\l^3.$ In addition, $\sb$ is called of
finite type if it has finite topology, finitely many singular points and
$\tilde{\sb}$ is finitely sheeted. Complete and proper maximal immersions with
isolated singularities in $\N$ are entire, and entire embedded maximal surfaces
in $\N$ with a finite number of singularities are of finite type.
  We classify complete flat Lorentzian 3-manifolds carrying entire maximal
surfaces of finite type, and deal with the topology, Weierstrass representation
and asymptotic behavior of this kind of surfaces.
  Finally, we construct new examples of periodic entire embedded maximal
surfaces in $\l^3$ with fundamental piece having finitely many singularities.
