1 The Gauss map of minimal surfaces in R3 -- ยง1.1 Minimal surfaces in Rm -- ยง1.2 The Gauss map of minimal surfaces in Bm -- ยง1.3 Enneper-Weierstrass representations of minimal surfaces in R3 -- ยง1.4 Sum to product estimates for meromorphic functions -- ยง1.5 The big Picard theorem -- ยง1.6 An estimate for the Gaussian curvature of minimal surfaces -- 2 The derived curves of a holomorphic curve -- ยง2.1 Holomorphic curves and their derived curves -- ยง2.2 Frenet frames -- ยง2.3 Contact functions -- ยง2.4 Nochka weights for hyperplanes in subgeneral position -- ยง2.5 Sum to product estimates for holomorphic curves -- ยง2.6 Contracted curves -- 3 The classical defect relations for holomorphic curves -- ยง3.1 The first main theorem for holomorphic curves -- ยง3.2 The second main theorem for holomorphic curves -- ยง3.3 Defect relations for holomorphic curves -- ยง3.4 Borelโ{128}{153}s theorem and its applications -- ยง3.5 Some properties of Wronskians -- ยง3.6 The second main theorem for derived curves -- 4 Modified defect relation for holomorphic curves -- ยง4.1 Some properties of currents on a Riemann surface -- ยง4.2 Metrics with negative curvature -- ยง4.3 Modified defect relation for holomorphic curves -- ยง4.4 The proof of the modified defect relation -- 5 The Gauss map of complete minimal surfaces in Rm -- ยง5.1 Complete minimal surfaces of finite total curvature -- ยง5.2 The Gauss maps of minimal surfaces of finite curvature -- ยง5.3 Modified defect relations for the Gauss map of minimal surfaces -- ยง5.4 The Gauss map of complete minimal surfaces in R3 and R4 -- ยง5.5 Examples