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In this paper, we will give an Enneper-type representation for spacelike andtimelike minimal surfaces in the Lorentz-Minkowski space $L^{3}$, using thecomplex and the paracomplex analysis (respectively). Then, we exhibit variousexamples of minimal surfaces in $L^{3}$ constructed via the Enneperrepresentation formula, that it is equivalent to the Weierstrass representationobtained by Kobayashi (for spacelike immersions) and by Konderak (for thetimelike ones).

Enneper representation of minimal surfaces in the three-dimensional Lorentz-Minkowski space