Electrical conduction in graphene is unlike that in any other material, particularly as the charge carriers in graphene have no mass and behave more like light than matter. The aim of this project is to study the conduction processes in graphene by a synergy of scanning probe microscopy and conduction measurements. Scanning probe microscopy allows nanometre-scale resolution of surfaces and has become an essential tool in contemporary nanoscience. One of graphene's unique properties is that conduction occurs through a surface (one atom thick) that is open to the environment. Sources of scattering that affect the conduction are therefore possible to directly detect by microscopy techniques [see, for example, F. V. Tikhonenko, D. W. Horsell, R. V. Gorbachev and A. K. Savchenko, Phys. Rev. Lett. 100, 056802 (2008)]. We will use them to detect and control topological, electrostatic and material characteristics of graphene that are directly related to the current flow. Atomic force probe measurements will allow us to see what influence the underlying substrate has on the topology of the crystal. Electrostatic force probe measurements will be used to construct an electrostatic map of the crystal showing the distribution of the potential in the presence of defects, charged impurities and chemical dopants. The scanning probe measurements will be performed at different carrier densities and combined with simultaneous measurements of the electrical conductance.