The simulation of high-resolution electron micrographs is a valuable tool for determining the atomic structure of objects by means of electron microscopical techniques. To account correctly for the process of image formation in a transmission electron microscope a theory solely based on the stationary wave function of the scattered electron proves to be insufficient to take the step from qualitative to quantitative image simulation in high-resolution electron microscopy. To avoid this shortcoming this thesis investigates a more realistic theoretical description of image formation based on the mutual coherence function of the scattered electron wave field. This more general concept allows to consider the influence of partially coherent illumination and of inelastic electron scattering on the recorded image intensity and on the diffraction pattern. Within the frame of validity of the high--energy approximation the coherence function approach can be used to derive a quite efficient numerical image simulation procedure. This new methods can be characterized as a true gerneralization of the conventional multislice method. In contrast to other approximation methods the coherence function multislice method does not violate the optical theorem of quantum mechanical scattering theory, even if inelastically scattered electrons are taken into account. This implies that the total probability current is conserved. The theoretical fundamentals of the coherence function approach are discussed in detail and the feasibility of the coherence function multislice method is demonstrated. A comparison between calculated and experimentally obtained diffraction patterns shows that the characteristic features of unfiltered electron diffraction patterns are very well reproduce. The coherence function multislice method can be employed to calculated zero-loss filtered and unfiltered diffraction patterns and images for the fixed-beam and the scanning tranmission electron microscope, respectively. The specimen structure can be either crystalline or amorphous. Additionally, realistic illumination and imaging conditions can be taken into account.