In this thesis we summarize a number of theoretical studies\ndealing with various properties of quantum dots.\nSmall quantum dots with a large level spacing\nare very well described by the Anderson impurity model.\nIn modern quantum dot experiments all parameters of this model can be tuned via external gate voltages. Thus, it should be possible to check our theoretical findings experimentally. \nWe are particularly interested in temperatures $T$ smaller than the so-called Kondo temperature $T_K$, $T<T_K$. The Kondo temperature $T_K$ is an energy scale below\nwhich a local spin inside the dot interacts strongly with the conduction electrons in its neighboring leads.\nConsequently we employ Wilson's numerical renormalization group method, a numerical technique which allows for an accurate calculation of properties of quantum dots in the Kondo regime.