At first, I will introcduce the basic theory about hyperbolic space and hyperbolic manifolds. Then I will disscuss the aymptotic Plateau problem (in hyperbolic 3-space), the minimal surfaces in quasi-Fuchsian 3-manifolds, the minimal surfaces in hyperbolic 3-manifolds with finite volume, and the reltation between the short geodesics and the number of (incompressible) minimal surfaces in hyperbolic 3-manifolds.

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