This thesis deals with certain phenomena in the field of triangle geometry. First, general definitions and theorems, which form the basis for the further chapters, will be proved. Among others the theorem of Pythagoras as well as the theorem of Ceva, which is less known, but still important in triangle geometry, will be presented. Then the existence of the well-known points orthocenter, circumcentre, incentre and centroid will be proved. In this context Euler's contribution in triangle geometry, especially the line named after him, will be discussed. In the last chapter of this thesis certain definitions, theorems and applications related to excircles, the theorem of Feuerbach in connection with the nine-point circle, Fermat's and Jacobi's points, Napoleon's triangle and the triangles of Hofstadt and Morley will be presented. The focus of this thesis is on geometrical and constructional argumentation. Therefore, this thesis is not only of interest for mathematicians, but also for interested laymen and advanced school education.