Two dimensional (2D) materials such as graphene and transition metal dichalcogenides (TMDs) exhibit fascinating properties, which are distinct from their corresponding 3D crystals. Examples include a transition from an indirect to a direct bandgap semiconductor in few layer and single layer MoS2, single photon emission from edge states in WSe2 and photoluminescence quantum yields close to unity. Potential applications in transistors and solar cells have already been demonstrated for some TMDs. Especially, the edges of some 2D materials exhibit novel physical properties that need to be understood better. Recently, single photon emission has been observed at the edges of WSe2 flakes. The effects are linked to defects at the edges. In this PhD project I plan to develop an atomic scale model of the defects at step edges and their influence on optical and vibrational properties. Furthermore, I will study the impact of locally varying strain on the properties of MoS2 flakes and I will perform model experiments to understand the effect of extrinsic and substrate induced doping on the optical and vibrational properties of MoS2 flakes. I will use scanning probe techniques such as scanning tunneling microscopy and Kelvin Probe force microscopy to study defects and strain in MoS2 on the nanometer scale. I will supplement these measurements with Photoluminescence and Raman measurements. Defects will be introduced via ion beam erosion at grazing where the sputtering yield at the step edges are much higher than on flat terraces. Ion implantation with subsequently annealing will be used change the strain in MoS2 and extrinsic doping will be carried out via alkali metals intercalation.I plan to have secondments in Aachen and Oldenburg, and throughout my thesis I will have support from a theory group at the UL who specialized on density functional theory of 2D materials.