I Criteria for starlikeness for holomorphic mappings -- II Criteria for convexity for holomorphic mappings -- III The growth theorem for holomorphic starlike mappings -- IV The growth theorem for holomorphic convex mappings -- V The distortion theorem for the linearinvariant family -- VI The distortion theorem for holomorphic convex and starlike mappings -- VII The geometrical properties for holomorphic convex mappings on the unit ball -- References -- List of symbols.