Observation of Superconductivity in Epitaxially Grown Atomic Layers : In Situ Electrical Transport Measurements This thesis presents first observations of superconductivity in one or two atomic scale thin layer materials. The thesis begins with a historical overview of superconductivity and the electronic structure of two dimensional materials and mentions that these key ingredients lead to the possibility of the two dimensional superconductor with high phase transition temperature and critical magnetic field. Thereafter the thesis moves its focus onto the implemented experiments in which mainly two different materials thallium deposited silicon surfaces and metal intercalated bilayer graphenes are used. The study of the first material is the first experimental demonstration of both a gigantic Rashba effect and superconductivity in the materials supposed to be superconductors without spatial inversion symmetry. The study of the latter material is relevant to superconductivity in a bilayer graphene which was a big experimental challenge for a decade and has been first achieved by the author. The description of the generic and innovative measurement technique highly effective in probing electric resistivity of ultra thin materials unstable in an ambient environment makes this thesis a valuable source for researchers not only in surface physics but also in nano materials science and other condensed matter physics. Introduction Fundamentals Experimental methods Thallium biatomic layer Thallium lead monatomiclayer compound Intercalation Compounds of Bilayer Graphene Conclusion.