1.The structure of complete embedded surfaces with constant curvature. 2.Some structure theorems. For complete constant mean curvature surfaces with boundary a convex curve. 3.Uniqueness, symmetry, and embedded of minimal surfaces and application. 4.A maximum principle at infinity for minimal surfaces and application. 5.A strict maximum principle for area minimizing hypersurfaces. 6.New minimal surfaces in S3. 7.Complete surface of finite total curvature. 8.Connection to complete surface of finite total curvature. 9.The Dirichlet problem at infinity for manifold of negative curvature. 10.The Dirichlet problem at infinite for a negatively curved manifold. 11.Embedded minimal surfaces in manifolds diffeomorphic to the three-dimensional ball on sphere. 12.Surfaces of mean curvature one in hyperbolic space.