Kondo insulators/semiconductors are a small group of materials showing unusual temperature-dependence of physical properties. At low temperature, a temperature-dependent narrow gap opens in the electronic density of states (DOS) at the Fermi level leading to insulating or semiconducting behaviour. The commonly adopted hybridization gap picture provides an overall description of the most common, cubic Kondo insulators. However, in systems with lower symmetry the situation is more complex, and far from being understood. Within this PhD thesis, the tetragonal compound CeRu4Sn6 is investigated which was classified as putative Kondo insulator by previous measurements on polycrystalline samples. In addition, previous measurements on single crystals revealed anisotropy of the magnetization and the specific heat in magnetic fields applied along different crystallographic directions. So, an opening of an anisotropic hybridization gap in CeRu4Sn6 was suggested. Therefore, a detailed investigations of the putative anisotropic Kondo insulator CeRu4Sn6 was of great interest to determine the nature of its behaviour accurately. Firstly, high-quality single crystals of CeRu4Sn6 were successfully grown. Next, a broad spectrum of physical properties measurements were performed to investigate mainly the electronic properties, the gap formation and crystalline electric field splitting. All electronic properties show distinct anisotropy between the tetragonal  axis and the basal (001) plane. The main origin of this behaviour is suggested to be due to anisotropic hybridization effects. Hence, CeRu4Sn6 is a potential candidate to investigate anisotropic hybridization in a tetragonal compound which was already started within this thesis.