"Topological insulators constitute a novel class of materials where the topological details of the bulk band structure induce a robust surface state on the edges of the material. While transport data for 2-dimensional topological insulators have recently become available, experiments on their 3-dimensional counterparts are mainly limited to photoelectron spectroscopy. At the same time, a plethora of interesting novel physical phenomena have been predicted to occur in such systems.In this proposal, we sketch an approach to tackle the transport and magnetic properties of the surface states in these materials. This starts with high quality layer growth, using molecular beam epitaxy, of bulk layers of HgTe, Bi2Se3 and Bi2Te3, which are the prime candidates to show the novel physics expected in this field. The existence of the relevant surface states will be assessed spectroscopically, but from there on research will focus on fabricating and characterizing nanostructures designed to elucidate the transport and magnetic properties of the topological surfaces using electrical, optical and scanning probe techniques. Apart from a general characterization of the Dirac band structure of the surface states, research will focus on the predicted magnetic monopole-like response of the system to an electrical test charge. In addition, much effort will be devoted to contacting the surface state with superconducting and magnetic top layers, with the final aim of demonstrating Majorana fermion behavior. As a final benefit, growth of thin high quality thin Bi2Se3 or Bi2Te3 layers could allow for a demonstration of the (2-dimensional) quantum spin Hall effect at room temperature - offering a road map to dissipation-less transport for the semiconductor industry."