"Topological insulators are the recently discovered class of materials that have a bulk electronic band gap, but also exhibit conducting surface states as a result of non-trivial band structure topology induced by strong spin-orbit interactions. These peculiar surface states are characterized by a number of novel properties such as graphene-like band dispersion and helical spin textures with no spin degeneracy which makes them immune to scattering. Due to these extraordinary properties, topological insulators are expected to find numerous technological applications, in particular in electronics and its next-day extensions - spintronics and quantum information processing. The project aims at exploring these novel electronic materials in silico; that is, by performing computer simulations using numerical methods of various levels of complexity. The global objective of the proposed research plan is to provide the theoretical support required to build a link between the fundamental physical properties of topological insulators and their prospective technological application by investigating materials science, chemistry and device-related aspects of these materials. In particular, the following three research directions will be explored: (i) understanding the structure-property relations and rational design of new materials with topologically non-trivial electronic structures, (ii) modeling realistic ""second generation"" topological insulators (bismuth chalcogenides Bi2Se3, Bi2Te3, and related materials), and (iii) investigating magnetic and transport properties of topological insulators and their interfaces related to the device applications. The proposed interdisciplinary program intends to make a strong impact in basic research and future technologies, and will eventually promote the rapidly expanding field of topological insulators in European science."