The intention of this booklet is a brief but general introduction into the treatment of the Finite Element Method (FEM). The FEM has become the leading method in computer-oriented mechanics, so that many scientific branches have grown up besides over the last decades. Nevertheless, the FEM today is a question of economy. On the one hand its industrial application is forced to reduce product development costs and time, on the other hand a large number of commercial FEM codes and a still growing number of software for effective pre- and postprocessors are available in the meantime.