Atomic Force Microscopy (AFM) is a powerful tool for the characterization and fabrication of two-dimensional materials, which are films of a few atomic layers with strong in-plane bonds and weak van der Waals interactions between the layers. The in-plane elasticity has been widely studied with nano-indentation where a suspended 2D film is bent substantially (~10nm to 1000nm). In this thesis we report on a novel AFM-based sub-Å-resolution indentation technique: Modulated nano-indentation (MoNI) or "Å-indentation". MoNI can allow for indentation below 1 Å, smaller than the inter-layer distance of most 2D materials. The perpendicular-to-the-plane elasticity of 2D materials can be detected with MoNI at extremely high precision while the in-plane covalent bonds are negligible. The inter-layer elasticity as well as intercalation properties of epitaxial graphene, graphene oxide and other 2D materials were carefully investigated. Furthermore, the fingerprint of a new ultra-hard phase of epitaxial graphene on SiC(0001), indicating possible diamondization at room temperature, has been observed and reported in this thesis.