Epitaxial growth of topological insulators (TIs) facilitates specific control of their electronic and spin- related properties by, e.g., utilizing lattice strain, or suitable interfacing with other materials. Extending this successful approach into the next funding period, project A08 will focus on three families of Sn- based TIs: (1) α-Sn, which we have recently established as a 3D topological material, in close analogy to the prototypical TI material HgTe. By varying strain and/or film thickness the topological charac- ter of the material can be widely controlled. The project will explore the corresponding topological phase diagram (Dirac semimetal vs. TI, quasi-2D vs. 3D regime) by systematic MBE film growth and subsequent spectroscopic experiments. (2) Stanene, a freestanding graphene-like variant of Sn, has recently been suggested to be a large-gap 2D-TI. Its experimental realization, however, is challenging as coupling to the substrate used for its real-world synthesis often destroys the topological character. Here we will employ a new concept (developed with theory project C05) to create quasi-freestanding stanene, and experimentally search for topological edge states. (3) (Pb,Sn)Te, a family of topologi- cal crystalline insulators (TCI) for which photoemission studies have often been impeded by strong intrinsic p-doping. This problem has recently been solved by a novel heterostructuring technique de- veloped in project A05, opening promising experimental opportunities for A08. The project will employ the versatility of angle- and spin-resolved photoelectron spectroscopy (ARPES, SARPES) as well as low-temperature scanning tunneling (STM) and spectroscopy (STS) to probe the various topological surface and edge states.